How do you find the antiderivative of #(e^(2x))/(1+(e^(4x))dx#?

1 Answer
Dec 12, 2016

Answer:

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

Explanation:

#inte^(2x)/(1+e^(4x))dx#

Let #u=e^(2x)# so #du=2e^(2x)dx#.

#=1/2int(2e^(2x))/(1+(e^(2x))^2)dx#

#=1/2int1/(1+u^2)du#

This is the arctangent integral:

#=1/2arctan(u)+C#

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

Another way to show this is to use the trigonometric substitution #e^(2x)=tan(theta)#.