∫ e x 1 + e x d x {\displaystyle \int e^{x}{\sqrt {1+e^{x}}}dx}
u = 1 + e x {\displaystyle u=1+e^{x}}
d u = e x d x {\displaystyle du=e^{x}dx}
∫ u d u {\displaystyle \int {\sqrt {u}}du}
u d u = 2 u 2 3 3 {\displaystyle {\sqrt {u}}du={\frac {2u^{\frac {2}{3}}}{3}}}
