常用不定积分

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$$\begin{array}{rl}\int k\mathrm{d}x=& kx+C(k\mathrm{是常数})\\ \int x^u\mathrm{d}x=& \frac{x^{u+1}}{u+1}+C(u\ne -1)\\ & \\ \int \frac{\mathrm{d}x}{x}=& \ln |x|+C\\ \int \frac{\mathrm{d}x}{1+x^2}=& \arcsin x+C\\ \int \cos x\mathrm{d}x=& \sin x+C\\ \int \sin x\mathrm{d}x=& -\cos x+C\\ \int \frac{\mathrm{d}x}{{\cos }^{2}x}=& \int {\sec }^x\mathrm{d}x=\tan x+C\\ \int \frac{\mathrm{d}x}{{\sin }^{2}x}=& \int {\csc }^{2}x\mathrm{d}x=\cot x+C\\ \int \sec x\tan x\mathrm{d}x=& \sec x+C\\ \int \csc x\cot x\mathrm{d}x=& -\csc x+C\\ \int e^x\mathrm{d}x=& e^x+C\\ \int a^x\mathrm{d}x=& \frac{a^x}{\ln a}+C\end{array}$$

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