数学计算--高等数学不定积分基本公式

2017-01-03 作者: xuzhiping 浏览: 463 次

摘要: 不定积分基本公式 \(\int kdx = kx+c\) \(\int x^ndx =\frac{x^(n+1)}{n+1}+c\) \(\int e^xdx =e^x+c\) \(\int a^xdx =a^x\times (\frac{1}{lna})+c....

不定积分基本公式

\(\int kdx = kx+c\)

\(\int x^ndx =\frac{x^(n+1)}{n+1}+c\)

\(\int e^xdx =e^x+c\)

\(\int a^xdx =a^x\times (\frac{1}{lna})+c\)

\(\int \frac{1}{x}dx =ln|x|+c\)

\(\int sinxdx =-cosx+c\)

\(\int cosxdx =sinx+c\)

\(\int tanxdx =-ln|cosx|+c\)

\(\int cotxdx =ln|sinx|+c\)

\(\int cscxdx =ln|cscx+cotx|+c\)

\(\int secxdx =ln|secx+tanx|+c\)

\(\int \frac{1}{sin^2x}dx =\int csc^2xdx=-cotx+c\)

\(\int \frac{1}{cos^2x}dx =\int sec^2xdx=tanx+c\)

\(\int \frac{1}{1+x^2}dx =arctanx+c\)

\(\int \frac{1}{\sqrt{1-x^2}}dx = arctanx+c\)

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