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Question Number 141526 by sarkor last updated on 20/May/21

Answered by rs4089 last updated on 20/May/21

$$\int (x+1)\sqrt{x^2+2x}dx$$$$\frac{1}{2}\int (2x+2)\sqrt{x^2+2x}dx$$$$let{x}^2+2x=t\Rightarrow (2x+2)dx=dt$$$$\frac{1}{2}\int \sqrt{t}dt=\frac{1}{2}\frac{t^{\frac{3}{2}}}{\frac{3}{2}}=\frac{1}{3}{t}^{\frac{3}{2}}=\frac{1}{3}\sqrt{{(x^2+2x)}^3}+C$$

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