Question

How to evaluate `int_0^2(e^(2x)/(e^x-1))`? Is there a way of not directly doing substitution?

Answer 1

`int_0^2 (e^(2x)*dx)/(e^x-1)=oo`

Explanation:

`int_0^2 (e^(2x)*dx)/(e^x-1)`

=`int_0^2 (e^x*e^x*dx)/(e^x-1)`

After using `u=e^x-1` and `du=e^x*dx` transforms,

`int_0^(e^2-1) ((u+1)*du)/u`

=`oo`