Integral de x^(1/In(x))

Resolución integral 4

[@VSN1001]

x^(1/lnx) = e^(lnx*(1/lnx))=e. Hence integral is ex+c

[@MartinPerez-oz1nk]

PADRISIMA ÍNTEGRAL !!!!, GRACIAS. !!!

[@venedem]

Good video, thanks

[@maxmax0]

Very decisive!

[@HenryBriskin]

Substitution Rule of Integration

[@alvargd6771]

x^(1/ln(x))=e^(ln(x)/ln(x))=e^1=e luego la integral es ex

[@Mini_Wolf.]

poderosa

[@ilskim]

There is a much easier way: log_a(b)=1/(log_b(a)), and therefore 1/ln(x) = 1/(log_e(x))=log_x(e). Since x^(log_x(e))=e, the integrand can be written as e (when the value of x is greater than 0 and is not 1).

[@jbteleco]

Of course, another way to solve the integral is to use the graphical method, if we graph x^(1/ln(x)) on a grapher, we observe a constant function with value e.

[@user-lu6yg3vk9z]

@@jbteleco? Why didn’t use e^ln

[@jbteleco]

@@user-lu6yg3vk9z I wanted to do it using the substitution method

[@aimsdaretosuccess]

Iam 140th subscriber

[@peep3879]

Hola, recién estoy aprendiendo los métodos de integración. No entiendo porque "e^u=x" al hacer el cambio de variables. Podría alguien explicar?

[@peep3879]

ah, ya lo entendí. tan solo aplicó la definición de logaritmo

[@anubis3060]

But if you differentiate to check the result, it does not give you what is inside the integral..

[@iziqx]

it does give you e and with some algebra u can turn e into x to the power of 1 over ln x as long as x is not 1

[@yimisbuenaventuracastro2877]

¿Cómo haces los videos?

[@jqn9156]

con la poya y los webos

[@aulaFICMA]

Es con manim, utiliza el lenguaje de programación python.

[@pabloluengomena2618]

Pero si derivas ex + C: (ex + C)' = (ex)' + C' = ex' + 0. Como "e" es una constante permanece igual y la derivada de x es 1. Por tanto quedaría solo "e" Pd: a lo mejor me equivoco yo. Aún asi buen video.

[@theelectro15]

esq lo que pasa esq x elevado a 1/lnx es igual a e

[@pabloluengomena2618]

@@theelectro15 Desconocía ese dato. Gracias.

[@alandavidacerocortes3046]

Si, yo coloque en otro comentario como se consigue

[@vbprogrammer95]

Hmmm... let's analyze what's inside the integral: x^(1/(ln x)). x must be > 1 for this to exist. Then let's set it equal to y and see what we can do with it: y = x^(1/(ln x)) Take the log of both sides: ln y = ln(x^(1/(ln x))) The log allows us to move the power in front: ln y = (1/(ln x)) * (ln x) thus ln y = (ln x)/(ln x) which means ln y = 1 and by appling the exponential function on both sides y = e So basically you're overcomplicating taking the integral of e...

[@user-my8wt8rn2q]

a much better solving method, use the fact that x=e^ln(x)