T17 指数函数与三角函数乘积的积分

:::{prf:theorem} :label: exp-sin-integration

$$\int e^{ax}\sin bx\mathrm{d}x=\frac{\left|\begin{array}{cc}(e^{ax}{)}^{\prime }& (\sin bx{)}^{\prime }\\ e^{ax}& \sin bx\end{array}\right|}{a^2+b^2}+C$$ $$\int e^{ax}\cos bx\mathrm{d}x=\frac{\left|\begin{array}{cc}(e^{ax}{)}^{\prime }& (\cos bx{)}^{\prime }\\ e^{ax}& \cos bx\end{array}\right|}{a^2+b^2}+C$$

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