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How do you find the integral of #e^(2x) sqrt(1 + e^(2x)) dx#?

1 Answer

Jun 9, 2015

#1/3 (1+e^(2x))^(3/2)# +C

Explanation:

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

Accordingly, #int e^(2x) sqrt(1+e^(2x) dx#=# 1/2int u^(1/2) du#

=#1/3 u^(3/2)# +C

=#1/3 (1+e^(2x))^(3/2)# +C

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