58:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
Taller:@0.175844:0.656768:0.236739:0.656768:0.236739:0.622820:0.175844:0.622820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Concibe la integración como proceso inverso, y realiza conexiones geométricas y físicas. (I.2.) (Ref. I.M.5.5.1.) :@0.256865:0.644794:0.756321:0.644794:0.756321:0.634365:0.256865:0.634365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.698006:0.133950:0.698006:0.133950:0.680870:0.115209:0.680870:0.000000:0.000000:0.000000
Resuelve:@0.148452:0.698006:0.216614:0.698006:0.216614:0.681382:0.148452:0.681382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 las siguientes integrales por cambio :@0.216614:0.698006:0.491923:0.698006:0.491923:0.681617:0.216614:0.681617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de variable.:@0.148452:0.714602:0.231965:0.714602:0.231965:0.698213:0.148452:0.698213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.148452:0.735195:0.167175:0.735195:0.167175:0.718295:0.148452:0.718295:0.000000:0.000000:0.000000
∫:@0.185579:0.742796:0.193841:0.742796:0.193841:0.717313:0.185579:0.717313:0.000000
=:@0.263687:0.735433:0.274723:0.735433:0.274723:0.718444:0.263687:0.718444:0.000000
+:@0.319070:0.735433:0.330107:0.735433:0.330107:0.718444:0.319070:0.718444:0.000000
∀ ∈⎡:@0.370896:0.735433:0.422379:0.735192:0.422379:0.718203:0.370896:0.718444:0.000000:0.000000:0.000000:0.000000
⎣:@0.414668:0.740384:0.422387:0.740384:0.422387:0.723396:0.414668:0.723396:0.000000
⎤:@0.450371:0.735197:0.458090:0.735197:0.458090:0.718208:0.450371:0.718208:0.000000
⎦:@0.450371:0.740384:0.458090:0.740384:0.458090:0.723396:0.450371:0.723396:0.000000
f:@0.201805:0.735555:0.207394:0.735555:0.207394:0.715489:0.201805:0.715489:0.000000
( ):@0.211756:0.735555:0.237086:0.735555:0.237086:0.715730:0.211756:0.715730:0.000000:0.000000:0.000000
( ):@0.290278:0.735555:0.315608:0.735555:0.315608:0.715730:0.290278:0.715730:0.000000:0.000000:0.000000
,    :@0.343350:0.735555:0.370870:0.735555:0.370870:0.715730:0.343350:0.715730:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.220441:0.734695:0.257691:0.734695:0.257691:0.716846:0.220441:0.716846:0.000000:0.000000:0.000000:0.000000
F x:@0.279483:0.734695:0.306300:0.734695:0.306300:0.716846:0.279483:0.716846:0.000000:0.000000:0.000000
c:@0.333439:0.734695:0.341802:0.734695:0.341802:0.716846:0.333439:0.716846:0.000000
x:@0.384319:0.734695:0.392461:0.734695:0.392461:0.716846:0.384319:0.716846:0.000000
a,b:@0.422535:0.734695:0.448045:0.734695:0.448045:0.716846:0.422535:0.716846:0.000000:0.000000:0.000000
(:@0.198426:0.734885:0.202866:0.734885:0.202866:0.719986:0.198426:0.719986:0.000000
x:@0.202866:0.735199:0.210329:0.735199:0.210329:0.718838:0.202866:0.718838:0.000000
3 + 2)⁸  2  =:@0.210329:0.735199:0.302596:0.735199:0.302596:0.718810:0.210329:0.718810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.258112:0.735199:0.287578:0.735199:0.287578:0.718838:0.258112:0.718838:0.000000:0.000000:0.000000:0.000000
 :@0.148449:0.831265:0.152263:0.831265:0.152263:0.814364:0.148449:0.814364:0.000000
b) :@0.148451:0.853637:0.168481:0.853637:0.168481:0.836736:0.148451:0.836736:0.000000:0.000000:0.000000
∫:@0.185579:0.861232:0.193841:0.861232:0.193841:0.835749:0.185579:0.835749:0.000000
=:@0.263687:0.853870:0.274723:0.853870:0.274723:0.836881:0.263687:0.836881:0.000000
+:@0.319070:0.853870:0.330107:0.853870:0.330107:0.836881:0.319070:0.836881:0.000000
∀ ∈⎡:@0.370896:0.853870:0.422379:0.853628:0.422379:0.836640:0.370896:0.836881:0.000000:0.000000:0.000000:0.000000
⎣:@0.414668:0.858821:0.422387:0.858821:0.422387:0.841832:0.414668:0.841832:0.000000
⎤:@0.450371:0.853633:0.458090:0.853633:0.458090:0.836645:0.450371:0.836645:0.000000
⎦:@0.450371:0.858821:0.458090:0.858821:0.458090:0.841832:0.450371:0.841832:0.000000
f:@0.201805:0.853992:0.207394:0.853992:0.207394:0.833925:0.201805:0.833925:0.000000
( ):@0.211756:0.853992:0.237086:0.853992:0.237086:0.834166:0.211756:0.834166:0.000000:0.000000:0.000000
( ):@0.290278:0.853992:0.315608:0.853992:0.315608:0.834166:0.290278:0.834166:0.000000:0.000000:0.000000
,    :@0.343350:0.853992:0.370870:0.853992:0.370870:0.834166:0.343350:0.834166:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.220441:0.853132:0.257691:0.853132:0.257691:0.835283:0.220441:0.835283:0.000000:0.000000:0.000000:0.000000
F x:@0.279483:0.853132:0.306300:0.853132:0.306300:0.835283:0.279483:0.835283:0.000000:0.000000:0.000000
c:@0.333439:0.853132:0.341802:0.853132:0.341802:0.835283:0.333439:0.835283:0.000000
x:@0.384319:0.853132:0.392461:0.853132:0.392461:0.835283:0.384319:0.835283:0.000000
a,b:@0.422535:0.853132:0.448045:0.853132:0.448045:0.835283:0.422535:0.835283:0.000000:0.000000:0.000000
(:@0.198426:0.853323:0.202866:0.853323:0.202866:0.838424:0.198426:0.838424:0.000000
x:@0.202866:0.853637:0.210329:0.853637:0.210329:0.837276:0.202866:0.837276:0.000000
2 + 3)⁹ :@0.210329:0.853637:0.258222:0.853637:0.258222:0.837248:0.210329:0.837248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xdx:@0.258222:0.853637:0.282123:0.853637:0.282123:0.837276:0.258222:0.837276:0.000000:0.000000:0.000000
 =:@0.282123:0.853637:0.297141:0.853637:0.297141:0.837248:0.282123:0.837248:0.000000:0.000000
 :@0.148449:0.928307:0.152263:0.928307:0.152263:0.911406:0.148449:0.911406:0.000000
Este método es una consecuencia de la derivación de funciones compuestas. Como su nombre indica, :@0.115209:0.167757:0.883861:0.167757:0.883861:0.151368:0.115209:0.151368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se trata de sustituir la variable   por otra variable   mediante una nueva función   tal que :@0.115209:0.184353:0.783760:0.184353:0.783760:0.167964:0.115209:0.167964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.340560:0.184353:0.348024:0.184353:0.348024:0.167992:0.340560:0.167992:0.000000
u:@0.479835:0.184353:0.489159:0.184353:0.489159:0.167992:0.479835:0.167992:0.000000
g:@0.713974:0.184353:0.723244:0.184353:0.723244:0.167992:0.713974:0.167992:0.000000
x = g u:@0.784626:0.184353:0.834611:0.184353:0.834611:0.167992:0.784626:0.167992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ), para :@0.820403:0.184353:0.883979:0.184353:0.883979:0.167964:0.820403:0.167964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
transformar el integrando  ( )  en otro más sencillo.:@0.115209:0.200949:0.499587:0.200949:0.499587:0.184560:0.115209:0.184560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x dx:@0.306854:0.200949:0.345516:0.200949:0.345516:0.184588:0.306854:0.184588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De esta manera, :@0.115209:0.224668:0.237439:0.224668:0.237439:0.208279:0.115209:0.208279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dx = g u du:@0.237439:0.224668:0.321949:0.224668:0.321949:0.208307:0.237439:0.208307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
’( ):@0.281058:0.224668:0.303355:0.224668:0.303355:0.208279:0.281058:0.208279:0.000000:0.000000:0.000000:0.000000
, con lo que quedaría que::@0.321949:0.224668:0.512452:0.224668:0.512452:0.208279:0.321949:0.208279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx dx:@0.128614:0.246627:0.175291:0.246627:0.175291:0.230266:0.128614:0.230266:0.000000:0.000000:0.000000:0.000000:0.000000
fg u:@0.204370:0.246627:0.241815:0.246627:0.241815:0.230266:0.204370:0.230266:0.000000:0.000000:0.000000:0.000000
g udu:@0.260390:0.246627:0.313904:0.246627:0.313904:0.230266:0.260390:0.230266:0.000000:0.000000:0.000000:0.000000:0.000000
∫:@0.194419:0.254048:0.201993:0.254048:0.201993:0.230689:0.194419:0.230689:0.000000
∫:@0.118654:0.254048:0.126228:0.254048:0.126228:0.230689:0.118654:0.230689:0.000000
=:@0.179709:0.247305:0.189826:0.247305:0.189826:0.231732:0.179709:0.231732:0.000000
⋅:@0.253677:0.247305:0.258284:0.247305:0.258284:0.231732:0.253677:0.231732:0.000000
():@0.135838:0.246627:0.157416:0.246627:0.157416:0.230238:0.135838:0.230238:0.000000:0.000000
(( )) '( ):@0.211594:0.246627:0.294149:0.246627:0.294149:0.230238:0.211594:0.230238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si el cambio de variable ha sido bien elegido, la última expresión será más fácil de integrar que la primera. :@0.115199:0.270554:0.883926:0.270554:0.883926:0.254165:0.115199:0.254165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una vez calculada esta, se deshace el cambio y tendremos así la integral pedida.:@0.115199:0.287150:0.699882:0.287150:0.699882:0.270761:0.115199:0.270761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuándo es aconsejable utilizar este método?:@0.115199:0.310869:0.448752:0.310869:0.448752:0.294480:0.115199:0.294480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Caso A: :@0.115199:0.334588:0.176600:0.334588:0.176600:0.317687:0.115199:0.317687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando aparezca en el integrando un producto o un cociente de funciones de modo que una de :@0.176194:0.334588:0.883815:0.334588:0.883815:0.318199:0.176194:0.318199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ellas “recuerda” a la derivada de la otra.:@0.115199:0.351184:0.394283:0.351184:0.394283:0.334795:0.115199:0.334795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Integración por sustitución o cambio de variable:@0.115891:0.141978:0.831302:0.141978:0.831302:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115891:0.381459:0.273013:0.381459:0.273013:0.363022:0.115891:0.363022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Integremos:@0.115891:0.401305:0.203901:0.401305:0.203901:0.384681:0.115891:0.384681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la siguiente expresión por cambio de variable.:@0.203901:0.401305:0.544123:0.401305:0.544123:0.384916:0.203901:0.384916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136518:0.428054:0.143981:0.428054:0.143981:0.411693:0.136518:0.411693:0.000000
x:@0.179767:0.428054:0.187231:0.428054:0.187231:0.411693:0.179767:0.411693:0.000000
x:@0.215619:0.428054:0.223082:0.428054:0.223082:0.411693:0.215619:0.411693:0.000000
dx:@0.255460:0.428054:0.272137:0.428054:0.272137:0.411693:0.255460:0.411693:0.000000:0.000000
x x x:@0.134057:0.461138:0.150997:0.459223:0.150997:0.442862:0.134057:0.444777:0.000000:0.000000:0.000000:0.000000:0.000000
dxdu x x:@0.174211:0.461138:0.230107:0.459223:0.230107:0.442862:0.174211:0.444777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x dx dx:@0.256140:0.461138:0.279161:0.459223:0.279161:0.442862:0.256140:0.444777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dx du:@0.294820:0.461138:0.348223:0.461138:0.348223:0.444777:0.294820:0.444777:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.383917:0.461138:0.391380:0.461138:0.391380:0.444777:0.383917:0.444777:0.000000
dx:@0.422597:0.461138:0.439274:0.461138:0.439274:0.444777:0.422597:0.444777:0.000000:0.000000
du:@0.470343:0.461138:0.488881:0.461138:0.488881:0.444777:0.470343:0.444777:0.000000:0.000000
∫:@0.119817:0.435476:0.127391:0.435476:0.127391:0.412116:0.119817:0.412116:0.000000
+:@0.155153:0.428732:0.165270:0.428732:0.165270:0.413159:0.155153:0.413159:0.000000
⋅:@0.202899:0.428732:0.207506:0.428732:0.207506:0.413159:0.202899:0.413159:0.000000
+:@0.226984:0.428732:0.237101:0.428732:0.237101:0.413159:0.226984:0.413159:0.000000
+ ++:@0.145417:0.461815:0.172286:0.459901:0.172286:0.444328:0.145417:0.446243:0.000000:0.000000:0.000000:0.000000
= ⋅ ⋅:@0.195300:0.461815:0.214522:0.459901:0.214522:0.444328:0.195300:0.446243:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.267500:0.461815:0.277617:0.461815:0.277617:0.446243:0.267500:0.446243:0.000000
=:@0.315928:0.461815:0.326044:0.461815:0.326044:0.446243:0.315928:0.446243:0.000000
+:@0.395295:0.461815:0.405412:0.461815:0.405412:0.446243:0.395295:0.446243:0.000000
=:@0.443723:0.461815:0.453840:0.461815:0.453840:0.446243:0.443723:0.446243:0.000000
(:@0.129344:0.428054:0.134228:0.428054:0.134228:0.411665:0.129344:0.411665:0.000000
4 )(:@0.168761:0.428054:0.213338:0.428054:0.213338:0.411665:0.168761:0.411665:0.000000:0.000000:0.000000:0.000000
2):@0.239855:0.428054:0.254265:0.428054:0.254265:0.411665:0.239855:0.411665:0.000000:0.000000
(2 ( (:@0.118089:0.461138:0.141244:0.459223:0.141244:0.442834:0.118089:0.444749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4) 4 )( )(:@0.159036:0.461138:0.220353:0.459223:0.220353:0.442834:0.159036:0.444749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;2( 2):@0.228194:0.461138:0.261281:0.459223:0.261281:0.442834:0.228194:0.444749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2):@0.280400:0.461138:0.294810:0.461138:0.294810:0.444749:0.280400:0.444749:0.000000:0.000000
(:@0.376776:0.461138:0.381660:0.461138:0.381660:0.444749:0.376776:0.444749:0.000000
2):@0.408196:0.461138:0.422606:0.461138:0.422606:0.444749:0.408196:0.444749:0.000000:0.000000
1:@0.459388:0.452176:0.468380:0.452176:0.468380:0.435787:0.459388:0.435787:0.000000
2:@0.458595:0.471621:0.467588:0.471621:0.467588:0.455232:0.458595:0.455232:0.000000
2:@0.145626:0.420393:0.150838:0.420393:0.150838:0.410895:0.145626:0.410895:0.000000
2:@0.194154:0.420393:0.199366:0.420393:0.199366:0.410895:0.194154:0.410895:0.000000
.:@0.276811:0.428149:0.280017:0.428149:0.280017:0.411760:0.276811:0.411760:0.000000
Hacemos:@0.115882:0.451868:0.186939:0.451868:0.186939:0.435244:0.115882:0.435244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el cambio  2 + 4  =  , :@0.186939:0.451868:0.349066:0.451868:0.349066:0.435479:0.186939:0.435479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.266454:0.451868:0.273918:0.451868:0.273918:0.435506:0.266454:0.435506:0.000000
x:@0.306608:0.451868:0.314071:0.451868:0.314071:0.435506:0.306608:0.435506:0.000000
u:@0.332499:0.451868:0.341823:0.451868:0.341823:0.435506:0.332499:0.435506:0.000000
derivamos:@0.348771:0.451868:0.429263:0.451868:0.429263:0.435244:0.348771:0.435244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los dos lados de la expresión y nos :@0.429263:0.451868:0.686826:0.451868:0.686826:0.435479:0.429263:0.435479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
queda::@0.115882:0.468464:0.166190:0.468464:0.166190:0.452075:0.115882:0.452075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2  + 4) 4) 4):@0.115882:0.492805:0.181195:0.492305:0.181195:0.475916:0.115882:0.476416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x x:@0.129758:0.492805:0.148546:0.492305:0.148546:0.475944:0.129758:0.476444:0.000000:0.000000:0.000000:0.000000:0.000000
dx = du:@0.170152:0.492805:0.223094:0.492805:0.223094:0.476444:0.170152:0.476444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;   ;2( ;2(:@0.223094:0.492805:0.260876:0.492305:0.260876:0.475916:0.223094:0.476416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.175057:0.459435:0.194247:0.459223:0.194247:0.442862:0.175057:0.443074:0.000000:0.000000:0.000000
dxdu:@0.169510:0.492517:0.222913:0.492517:0.222913:0.476156:0.169510:0.476156:0.000000:0.000000:0.000000:0.000000
x x:@0.251439:0.492517:0.270629:0.492305:0.270629:0.475944:0.251439:0.476156:0.000000:0.000000:0.000000
dx du du:@0.290117:0.492517:0.355249:0.492305:0.355249:0.475944:0.290117:0.476156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.379218:0.492517:0.398408:0.492305:0.398408:0.475944:0.379218:0.476156:0.000000:0.000000:0.000000
dx dx:@0.417898:0.492517:0.446310:0.492305:0.446310:0.475944:0.417898:0.476156:0.000000:0.000000:0.000000:0.000000:0.000000
du du:@0.465644:0.492517:0.495915:0.492305:0.495915:0.475944:0.465644:0.476156:0.000000:0.000000:0.000000:0.000000:0.000000
∫ ∫:@0.115107:0.466857:0.134407:0.466643:0.134407:0.443283:0.115107:0.443497:0.000000:0.000000:0.000000
++:@0.222275:0.460113:0.244117:0.459901:0.244117:0.444328:0.222275:0.444540:0.000000:0.000000
++:@0.140714:0.493195:0.162556:0.492983:0.162556:0.477410:0.140714:0.477622:0.000000:0.000000
==:@0.190598:0.493195:0.212440:0.492983:0.212440:0.477410:0.190598:0.477622:0.000000:0.000000
++:@0.262797:0.493195:0.284639:0.492983:0.284639:0.477410:0.262797:0.477622:0.000000:0.000000
==:@0.311225:0.493195:0.333067:0.492983:0.333067:0.477410:0.311225:0.477622:0.000000:0.000000
++:@0.390593:0.493195:0.412421:0.492983:0.412421:0.477410:0.390593:0.477622:0.000000:0.000000
==:@0.439021:0.493195:0.460849:0.492983:0.460849:0.477410:0.439021:0.477622:0.000000:0.000000
2):@0.235156:0.459435:0.249566:0.459435:0.249566:0.443046:0.235156:0.443046:0.000000:0.000000
(2 (2:@0.113386:0.492517:0.139806:0.492305:0.139806:0.475916:0.113386:0.476129:0.000000:0.000000:0.000000:0.000000:0.000000
2)2):@0.275697:0.492517:0.301822:0.492305:0.301822:0.475916:0.275697:0.476129:0.000000:0.000000:0.000000:0.000000
( (:@0.372073:0.492517:0.388672:0.492305:0.388672:0.475916:0.372073:0.476129:0.000000:0.000000:0.000000
2)2):@0.403492:0.492517:0.429594:0.492305:0.429594:0.475916:0.403492:0.476129:0.000000:0.000000:0.000000:0.000000
11:@0.454684:0.483555:0.475375:0.483347:0.475375:0.466958:0.454684:0.467167:0.000000:0.000000
22:@0.453892:0.503001:0.474583:0.502792:0.474583:0.486403:0.453892:0.486612:0.000000:0.000000
2 2:@0.140915:0.451773:0.157854:0.451561:0.157854:0.442063:0.140915:0.442275:0.000000:0.000000:0.000000
2 2:@0.189444:0.451773:0.206382:0.451561:0.206382:0.442063:0.189444:0.442275:0.000000:0.000000:0.000000
  :@0.345973:0.492817:0.354044:0.492817:0.354044:0.476428:0.345973:0.476428:0.000000:0.000000
⇒  :@0.354044:0.493494:0.381446:0.493494:0.381446:0.477921:0.354044:0.477921:0.000000:0.000000:0.000000
dxdu:@0.181237:0.492305:0.234640:0.492305:0.234640:0.475944:0.181237:0.475944:0.000000:0.000000:0.000000:0.000000
dx:@0.301846:0.492305:0.318523:0.492305:0.318523:0.475944:0.301846:0.475944:0.000000:0.000000
4:@0.175777:0.459223:0.184770:0.459223:0.184770:0.442834:0.175777:0.442834:0.000000
Cambiamos:@0.115891:0.520105:0.207163:0.520105:0.207163:0.503481:0.115891:0.503481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la integral en función de  , e :@0.207163:0.520105:0.423041:0.520105:0.423041:0.503716:0.207163:0.503716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.393501:0.520105:0.402825:0.520105:0.402825:0.503744:0.393501:0.503744:0.000000
integramos:@0.423041:0.520105:0.510515:0.520105:0.510515:0.503481:0.423041:0.503481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.510515:0.520105:0.513721:0.520105:0.513721:0.503716:0.510515:0.503716:0.000000
∫:@0.122119:0.556976:0.027828:0.556976:0.027828:0.533622:0.122119:0.533622:0.000000
∫:@0.294265:0.556976:0.199973:0.556976:0.199973:0.533622:0.294265:0.533622:0.000000
∫:@0.396128:0.556976:0.301837:0.556976:0.301837:0.533622:0.396128:0.533622:0.000000
∫:@0.122119:0.598105:0.129691:0.598105:0.129691:0.574751:0.122119:0.574751:0.000000
+:@0.158599:0.552394:0.168714:0.552394:0.168714:0.536825:0.158599:0.536825:0.000000
⋅:@0.205339:0.552394:0.209945:0.552394:0.209945:0.536825:0.205339:0.536825:0.000000
+:@0.228627:0.552394:0.189790:0.552394:0.189790:0.536825:0.228627:0.536825:0.000000
=:@0.277567:0.552394:0.238730:0.552394:0.238730:0.536825:0.277567:0.536825:0.000000
=:@0.359953:0.552394:0.321116:0.552394:0.321116:0.536825:0.359953:0.536825:0.000000
⋅:@0.386331:0.552394:0.390937:0.552394:0.390937:0.536825:0.386331:0.536825:0.000000
= ⋅⎜:@0.445784:0.552394:0.484989:0.553735:0.484989:0.538166:0.445784:0.536825:0.000000:0.000000:0.000000:0.000000
⎛:@0.477914:0.540890:0.484989:0.540890:0.484989:0.525321:0.477914:0.525321:0.000000
⎝:@0.477914:0.564811:0.484989:0.564811:0.484989:0.549242:0.477914:0.549242:0.000000
⎞:@0.505918:0.540890:0.512993:0.540890:0.512993:0.525321:0.505918:0.525321:0.000000
⎠:@0.505918:0.564811:0.512993:0.564811:0.512993:0.549242:0.505918:0.549242:0.000000
⎟+:@0.505918:0.553735:0.524083:0.552394:0.524083:0.536825:0.505918:0.538166:0.000000:0.000000
+:@0.158581:0.593516:0.168695:0.593516:0.168695:0.577947:0.158581:0.577947:0.000000
⋅:@0.205321:0.593516:0.209927:0.593516:0.209927:0.577947:0.205321:0.577947:0.000000
+:@0.228608:0.593516:0.189772:0.593516:0.189772:0.577947:0.228608:0.577947:0.000000
=:@0.277548:0.593516:0.238712:0.593516:0.238712:0.577947:0.277548:0.577947:0.000000
⋅:@0.304660:0.593516:0.309266:0.593516:0.309266:0.577947:0.304660:0.577947:0.000000
+:@0.335391:0.593516:0.306189:0.593516:0.306189:0.577947:0.335391:0.577947:0.000000
+:@0.374706:0.593516:0.345505:0.593516:0.345505:0.577947:0.374706:0.577947:0.000000
(:@0.133617:0.551717:0.138499:0.551717:0.138499:0.535331:0.133617:0.535331:0.000000
4 ) (:@0.171249:0.551717:0.215961:0.551717:0.215961:0.535331:0.171249:0.535331:0.000000:0.000000:0.000000:0.000000:0.000000
2):@0.240545:0.551717:0.254952:0.551717:0.254952:0.535331:0.240545:0.535331:0.000000:0.000000
1:@0.326805:0.543158:0.335796:0.543158:0.335796:0.526773:0.326805:0.526773:0.000000
2:@0.326013:0.562682:0.335004:0.562682:0.335004:0.546297:0.326013:0.546297:0.000000
1:@0.375259:0.543158:0.384250:0.543158:0.384250:0.526773:0.375259:0.526773:0.000000
2:@0.374467:0.562682:0.383457:0.562682:0.383457:0.546297:0.374467:0.546297:0.000000
1:@0.461094:0.543158:0.470084:0.543158:0.470084:0.526773:0.461094:0.526773:0.000000
2:@0.460302:0.562682:0.469292:0.562682:0.469292:0.546297:0.460302:0.546297:0.000000
3:@0.491124:0.562682:0.500115:0.562682:0.500115:0.546297:0.491124:0.546297:0.000000
(:@0.133599:0.592852:0.138481:0.592852:0.138481:0.576467:0.133599:0.576467:0.000000
4 ) (:@0.171230:0.592852:0.215942:0.592852:0.215942:0.576467:0.171230:0.576467:0.000000:0.000000:0.000000:0.000000:0.000000
2):@0.240526:0.592852:0.254933:0.592852:0.254933:0.576467:0.240526:0.576467:0.000000:0.000000
1:@0.293238:0.584294:0.302228:0.584294:0.302228:0.567908:0.293238:0.567908:0.000000
6:@0.292483:0.603804:0.301473:0.603804:0.301473:0.587419:0.292483:0.587419:0.000000
(:@0.310434:0.592844:0.315317:0.592844:0.315317:0.576459:0.310434:0.576459:0.000000
4):@0.348066:0.592844:0.373472:0.592844:0.373472:0.576459:0.348066:0.576459:0.000000:0.000000
2:@0.149911:0.544057:0.155122:0.544057:0.155122:0.534561:0.149911:0.534561:0.000000
2:@0.196651:0.544057:0.201862:0.544057:0.201862:0.534561:0.196651:0.534561:0.000000
2:@0.316039:0.544057:0.321250:0.544057:0.321250:0.534561:0.316039:0.534561:0.000000
2:@0.417890:0.544057:0.423101:0.544057:0.423101:0.534561:0.417890:0.534561:0.000000
3:@0.496817:0.535491:0.502028:0.535491:0.502028:0.525995:0.496817:0.525995:0.000000
2:@0.149911:0.585183:0.155122:0.585183:0.155122:0.575687:0.149911:0.575687:0.000000
2:@0.196651:0.585183:0.201862:0.585183:0.201862:0.575687:0.196651:0.575687:0.000000
2:@0.326717:0.585183:0.331927:0.585183:0.331927:0.575687:0.326717:0.575687:0.000000
x:@0.140805:0.551717:0.148266:0.551717:0.148266:0.535359:0.140805:0.535359:0.000000
x:@0.182258:0.551717:0.189719:0.551717:0.189719:0.535359:0.182258:0.535359:0.000000
x:@0.218266:0.551717:0.225728:0.551717:0.225728:0.535359:0.218266:0.535359:0.000000
dx:@0.256421:0.551717:0.273094:0.551717:0.273094:0.535359:0.256421:0.535359:0.000000:0.000000
u:@0.306196:0.551717:0.315518:0.551717:0.315518:0.535359:0.306196:0.535359:0.000000
du:@0.338070:0.551717:0.356604:0.551717:0.356604:0.535359:0.338070:0.535359:0.000000:0.000000
u du:@0.408048:0.551717:0.442443:0.551717:0.442443:0.535359:0.408048:0.535359:0.000000:0.000000:0.000000:0.000000
u:@0.486981:0.543158:0.496304:0.543158:0.496304:0.526800:0.486981:0.526800:0.000000
c:@0.526297:0.551717:0.533961:0.551717:0.533961:0.535359:0.526297:0.535359:0.000000
x:@0.140823:0.592839:0.148285:0.592839:0.148285:0.576481:0.140823:0.576481:0.000000
x:@0.182276:0.592839:0.189737:0.592839:0.189737:0.576481:0.182276:0.576481:0.000000
x:@0.218285:0.592839:0.225746:0.592839:0.225746:0.576481:0.218285:0.576481:0.000000
dx:@0.256439:0.592839:0.273113:0.592839:0.273113:0.576481:0.256439:0.576481:0.000000:0.000000
x:@0.317624:0.592839:0.325085:0.592839:0.325085:0.576481:0.317624:0.576481:0.000000
x:@0.359077:0.592839:0.366538:0.592839:0.366538:0.576481:0.359077:0.576481:0.000000
c:@0.387025:0.592839:0.394689:0.592839:0.394689:0.576481:0.387025:0.576481:0.000000
M.5.1.67. Reconocer la derivación y la integración como procesos inversos.:@0.125388:0.074999:0.470769:0.074999:0.470769:0.064570:0.125388:0.064570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16:@0.048299:0.122645:0.082213:0.122645:0.082213:0.065614:0.048299:0.065614:0.000000:0.000000
c) :@0.540986:0.697725:0.558621:0.697725:0.558621:0.680825:0.540986:0.680825:0.000000:0.000000:0.000000
∫:@0.578116:0.705322:0.586378:0.705322:0.586378:0.679839:0.578116:0.679839:0.000000
=:@0.656224:0.697959:0.667261:0.697959:0.667261:0.680971:0.656224:0.680971:0.000000
+:@0.711607:0.697959:0.722644:0.697959:0.722644:0.680971:0.711607:0.680971:0.000000
∀ ∈⎡:@0.763433:0.697959:0.814916:0.697718:0.814916:0.680729:0.763433:0.680971:0.000000:0.000000:0.000000:0.000000
⎣:@0.807205:0.702910:0.814925:0.702910:0.814925:0.685922:0.807205:0.685922:0.000000
⎤:@0.842908:0.697723:0.850627:0.697723:0.850627:0.680734:0.842908:0.680734:0.000000
⎦:@0.842908:0.702910:0.850627:0.702910:0.850627:0.685922:0.842908:0.685922:0.000000
f:@0.594342:0.698081:0.599931:0.698081:0.599931:0.678015:0.594342:0.678015:0.000000
( ):@0.604293:0.698081:0.629623:0.698081:0.629623:0.678256:0.604293:0.678256:0.000000:0.000000:0.000000
( ):@0.682815:0.698081:0.708145:0.698081:0.708145:0.678256:0.682815:0.678256:0.000000:0.000000:0.000000
,    :@0.735887:0.698081:0.763408:0.698081:0.763408:0.678256:0.735887:0.678256:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.612978:0.697221:0.650228:0.697221:0.650228:0.679373:0.612978:0.679373:0.000000:0.000000:0.000000:0.000000
F x:@0.672020:0.697221:0.698837:0.697221:0.698837:0.679373:0.672020:0.679373:0.000000:0.000000:0.000000
c:@0.725976:0.697221:0.734339:0.697221:0.734339:0.679373:0.725976:0.679373:0.000000
x:@0.776856:0.697221:0.784998:0.697221:0.784998:0.679373:0.776856:0.679373:0.000000
a,b:@0.815072:0.697221:0.840583:0.697221:0.840583:0.679373:0.815072:0.679373:0.000000:0.000000:0.000000
(2:@0.590963:0.697411:0.603578:0.697411:0.603578:0.682512:0.590963:0.682512:0.000000:0.000000
x:@0.603576:0.697725:0.611039:0.697725:0.611039:0.681364:0.603576:0.681364:0.000000
2 √ 3 + 1  =:@0.611039:0.697725:0.702831:0.697725:0.702831:0.681336:0.611039:0.681336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.630389:0.697725:0.637852:0.697725:0.637852:0.681364:0.630389:0.681364:0.000000
dx:@0.671080:0.697725:0.687812:0.697725:0.687812:0.681364:0.671080:0.681364:0.000000:0.000000
 :@0.540981:0.793791:0.544795:0.793791:0.544795:0.776890:0.540981:0.776890:0.000000
d) :@0.540986:0.821508:0.561054:0.821508:0.561054:0.804607:0.540986:0.804607:0.000000:0.000000:0.000000
∫:@0.578116:0.829106:0.586378:0.829106:0.586378:0.803623:0.578116:0.803623:0.000000
=:@0.656224:0.821742:0.667261:0.821742:0.667261:0.804753:0.656224:0.804753:0.000000
+:@0.711607:0.821742:0.722644:0.821742:0.722644:0.804753:0.711607:0.804753:0.000000
∀ ∈⎡:@0.763433:0.821742:0.814916:0.821500:0.814916:0.804512:0.763433:0.804753:0.000000:0.000000:0.000000:0.000000
⎣:@0.807205:0.826694:0.814925:0.826694:0.814925:0.809706:0.807205:0.809706:0.000000
⎤:@0.842908:0.821507:0.850627:0.821507:0.850627:0.804518:0.842908:0.804518:0.000000
⎦:@0.842908:0.826694:0.850627:0.826694:0.850627:0.809706:0.842908:0.809706:0.000000
f:@0.594342:0.821864:0.599931:0.821864:0.599931:0.801797:0.594342:0.801797:0.000000
( ):@0.604293:0.821864:0.629623:0.821864:0.629623:0.802039:0.604293:0.802039:0.000000:0.000000:0.000000
( ):@0.682815:0.821864:0.708145:0.821864:0.708145:0.802039:0.682815:0.802039:0.000000:0.000000:0.000000
,    :@0.735887:0.821864:0.763408:0.821864:0.763408:0.802039:0.735887:0.802039:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.612978:0.821004:0.650228:0.821004:0.650228:0.803155:0.612978:0.803155:0.000000:0.000000:0.000000:0.000000
F x:@0.672020:0.821004:0.698837:0.821004:0.698837:0.803155:0.672020:0.803155:0.000000:0.000000:0.000000
c:@0.725976:0.821004:0.734339:0.821004:0.734339:0.803155:0.725976:0.803155:0.000000
x:@0.776856:0.821004:0.784998:0.821004:0.784998:0.803155:0.776856:0.803155:0.000000
a,b:@0.815072:0.821004:0.840583:0.821004:0.840583:0.803155:0.815072:0.803155:0.000000:0.000000:0.000000
(:@0.590963:0.821194:0.595403:0.821194:0.595403:0.806295:0.590963:0.806295:0.000000
x:@0.595403:0.821508:0.602866:0.821508:0.602866:0.805147:0.595403:0.805147:0.000000
3 + 8)⁷  2  =:@0.602866:0.821508:0.694451:0.821508:0.694451:0.805119:0.602866:0.805119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x dx:@0.649967:0.821508:0.679433:0.821508:0.679433:0.805147:0.649967:0.805147:0.000000:0.000000:0.000000:0.000000
 :@0.540986:0.917573:0.544801:0.917573:0.544801:0.900673:0.540986:0.900673:0.000000
Shutterstock, 196361828.:@0.896371:0.612563:0.896371:0.524738:0.882475:0.524738:0.882475:0.612563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000