I was doing this equation$\displaystyle \int e^x\aqrt{1-e^2x}dx$ and I used the substitution $\displaystyle e^x=sinu$ which gave me

$\displaystyle \frac{sin(arcsin(e^x))(cos(arcsin(e^x))}{2}+\frac{ arcsin(e^x)}{2}+C$

which simplifies to $\displaystyle \frac{e^x\sqrt{1-exp(2x)}}{2}+\frac{arcsin(e^x)}{2}+C$ but i cant see how the first term of this was obtained from the first line here. If some one could help youd be od great help!!!