Evaluate the integral? : # int e^(2x)/(1+e^(2x))^2 dx #

1 Answer
Steve M
Feb 1, 2017

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

Explanation:

We want to find;

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

Let #u =1+e^(2x) => (du)/dx = 2e^(2x) #

Substituting into the integral we get:

# int \ e^(2x)/(1+e^(2x))^2 \ dx = int \ (1/2)/u^2 \ du#
# " " = 1/2int \ 1/u^2 \ du#
# " " = -1/2 1/u + C#
# " " = -1/(2(1+e^(2x))) + C#

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