How to work out the integral $\int e^x·\sqrt{1+e^x}$ $\int e^x·\sqrt{1+e^x}\,dx$
Can someone explain to me how to work this integral out?
I tried integration by parts, however, that does not give a clear answer.
I got a hint from our professor that we should use substitution, but if I substitute "$ 1+e^x$" for example, I still can't calculate it by integration by parts...

Substitute $1+e^{ x }=u$ then $du={ e }^{ x }dx$
$$\\ \\ \int  e^{ x }\sqrt { 1+e^{ x } } \,dx=\int  \sqrt { u } \,du=\frac { 2u\sqrt { u }  }{ 3 } +C=\\ =\frac { 2 }{ 3 } { \left( { e }^{ x }+1 \right)  }^{ \frac { 3 }{ 2 }  }+C$$
