Question

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

Answer 1

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

Explanation:

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`.