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$\begin{array}{lll} \int \frac{1}{x}dx=ln|x|+C & \int a^xdx=\frac{a^x}{lna}+C~[a>0,a\not=1] & \int e^xdx=e^x+C & \\ \int sinxdx=-cosx+C & \int cosxdx=sinx & \int tanxdx=-ln|cosx|+C \\ \int cotxdx=ln|sinx|+C & \int secxdx=ln|secx+tanx|+C & \int cscxdx=ln|cscx-cotx|+C \\ \int sec^2xdx=tanx+C & \int \csc^2xdx=-cotx+C & \int \frac{1}{a^2+x^2}dx=\frac{1}{a}arctan\frac{x}{a}+C \\ \int \frac{1}{a^2-x^2}dx=\frac{1}{2a}ln|\frac{a+x}{a-x}|+C & \int \frac{1}{\sqrt{a^2-x^2}}dx=arcsin\frac{x}{a}+C & \int \frac{1}{\sqrt{x^2\pm a^2}}=ln|x+\sqrt{x^2+a^2}|+C \\ \int x^\alpha dx=\frac{1}{\alpha+1}x^{\alpha+1}+C~[\alpha\not=-1] \end{array} \\ 华莱士公式： \int_0^{\frac{\pi}{2}}sin^nxdx=\int_0^{\frac{\pi}{2}}cos^nxdx=\begin{cases}\frac{n-1}{n}* \frac{n-3}{n-2}*...*\frac{2}{3}\quad (n为奇数) \\ \frac{n-1}{n}* \frac{n-3}{n-2}*...*\frac{1}{2}*\frac{\pi}{2}\quad (n为偶数) \end{cases} \\ \int xsinxdx=sinx-xcosx \\$

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