5.5 The Substitution Rule/11

$\int (x+1){\sqrt {2x+x^{2}}}dx$

${\begin{aligned}u&=2x+x^{2}\\[2ex]du&=2+2xdx\\[2ex]{\frac {1}{2}}du&=x+1\end{aligned}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int (x+1)\sqrt{2x+x^{2}}dx = \frac{1}{2}\int\sqrt{u}du = \frac{1}{2}\int u^{\frac{1}{2}}du \\[2ex] &= \frac{1]{2}\left(\frac{2u^{3}{2}}{3})\right + C \end{align} } &= \frac{1}{3}\left(u)\right^\frac{3}{2} + C