Question

Evaluate :

$\int e^x\sqrt{e^x+1}dx$

Answer 1

$I=\int e^x\sqrt{e^x+1}dx$

Let $e^x+1=t$

$e^{x}dx=dt$

Therefore,

$I=\int \sqrt{t}dt$

$I=\frac{2}{3}{t}^{3/2}+C$

$I=\frac{2}{3}(e^x+1{)}^{3/2}+C$