How do you find the antiderivative of #e^(2x)*( tan(e^(2x)) )^2#?
1 Answer
Oct 22, 2016
Explanation:
#I=inte^(2x)tan^2(e^(2x))dx#
Let
#I=1/2inttan^2(e^(2x))(2e^(2x)dx)#
#I=1/2inttan^2(u)du#
We can integrate this using the identity
#I=1/2int(sec^2(u)-1)du#
#I=1/2intsec^2(u)du-1/2intdu#
These are both common integrals:
#I=1/2tan(u)-1/2u+C#
With
#I=1/2tan(e^(2x))-1/2e^(2x)+C#