> [!question] 题干 > 求不定积分$\int \cos{x}e^{\sin{x}}dx$
> [!done]- 解 > $ > \begin{aligned} > \int \cos{x}e^{\sin{x}}dx&=\int e^{\sin{x}}d(\sin{x})&&根据d(\sin{x})=\cos{x} dx\\ > &=\int d(e^{\sin{x}})&&根据d(e^x)=e^xdx\\ > &=e^{\sin{x}}+C > \end{aligned} > $
百科词条
题型：凑微分法：例3
question 题干 求不定积分$\int \cos x e^ \sin x dx$ done - 解 $ \begin aligned \int \cos x e^ \sin x dx&=\int e^ \sin x d \sin x &&根据d \sin x =\cos x dx\\ &=\int d e^ \sin x &&根据d