Question

∫ [(e^x)/(1+e^(2x))] dx

Answer 1

Use u substitution and set u equal to the denominator.

Answer 2

thank u

Answer 3

No problem.

Answer 4

take e^x as some variable t => e^x=t
differentiate it on both sides u get e^x.dx=dt
in the question e^2x can be written as (e^x)^2 so it wil become (t)^2
leave numerator as it is and substitute dx=dt/e^x
then u wil get it in standard form.
and answer is \[\tan^{e^-x} \]

Answer 5

thanks i was having problems with just setting the bottom to U

Answer 6

u hav to take the variable according to the question.
in some questions u r way of taking variable is right and in some its not u hav to look out for the variable which gives u the answer in minimum no of steps for that particular question. it may not be applicable for other questions

Answer 7

I would just use the u substitution no need for change of variable to complicate things.