How do you find the antiderivative of #(e^(2x))/(1+e^(2x))#?
1 Answer
Feb 22, 2017
# int \ e^(2x)/(1+e^(2x)) \ dx = 1/2ln|1+e^(2x)| + c#
Explanation:
We want to find
A trivial substitution can be used to simplify the denominator; Let:
# u = 1+e^(2x) #
Then
If we substitute this into the integral we get;
# int \ e^(2x)/(1+e^(2x)) \ dx = int \ (1/2)/(u) \ du#
# " " = 1/2ln|u| + c#
And if we undo the substitution we get:
# int \ e^(2x)/(1+e^(2x)) \ dx = 1/2ln|1+e^(2x)| + c#