How do you find the antiderivative of #(e^(2x))/(1+(e^(4x))dx#?
1 Answer
Dec 12, 2016
Explanation:
#inte^(2x)/(1+e^(4x))dx#
Let
#=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