> [!question] 题干 > 求不定积分$\int xe^{-x^2}dx$
> [!done]- 解 > $ > \begin{aligned} > \int xe^{-x^2}dx&=\frac{1}{2}\int e^{-x^2}\cdot 2xdx\\ > &=\frac{1}{2}\int e^{-x^2}d(x^2)&&根据d(e^x)=e^xdx\\ > &=-\frac{1}{2}\int d(e^{-x^2})\\ > &=-\frac{1}{2}e^{-x^2}+C > \end{aligned} > $