Question

intergrate(e^5x)/((e^10x)+4)dx

Answer 1

Let e^5x = u

Then
5 e^5x dx = du
The integral becomes
INT (1/5)u/[u^2 +4] du
Now let v = u^2 + 4
dv = 2u du
The integral becomes
(1/10) INT (1/v)dv
= (1/10)ln v = (1/10) ln(u^2 + 4)
= (1/10)ln(e^10x + 4)