How do you find the antiderivative of #[e^(2x)/(4+e^(4x))]#?

1 Answer
Aug 3, 2016

Answer:

#1/4arctan(e^(2x)/2)+C#.

Explanation:

Let, #I = inte^(2x)/(4+e^(4x))dx#.

We take subst. #e^(2x)=t rArr e^(2x)*2dx=dt#.

Therefore, #I=1/2int(2*e^(2x)*dx)/{4+(e^(2x))^2}#,

#=1/2intdt/(4+t^2) = 1/2*1/2*arctan(t/2)#.

Hence, #I=1/4arctan(e^(2x)/2)+C#.