How do you evaluate the integral $int e^x(e^x+1)^3$ ?

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Answer 1 · 2017-01-19T14:09:08

$1/4(e^x+1)^4+C$ .

Suppose that (e^x+1)=t :. e^xdx=dt#

Hence, $inte^x(e^x+1)^3dx=int(e^x+1)^3e^xdx$

$=t^3dt=t^4/4$

$=1/4(e^x+1)^4+C$ .

How do you evaluate the integral int e^x(e^x+1)^3int e^x(e^x+1)^3?