常用积分公式

2021-03-15  本文已影响0人  出题老头

\int x^kdx=\frac{1}{k+1}x^{k+1}+C
\int \frac{1}{x^2}dx=-\frac{1}{x}+C
\int \frac{1}{\sqrt x}dx=2\sqrt x+C
\int \frac{1}{x}dx=\ln x+C
\int a^xdx = \frac{a^x}{\ln a}+C
\int e^xdx=e^x+C
\int \sin xdx=-\cos x+C
\int \cos xdx = \sin x +C
\int \tan x dx = -\ln \cos x+C
\int \cot xdx=\ln \sin x+C
\int \sec xdx = \ln( \sec x+\ tan x)+C
\int \csc xdx = \ln (\csc x-\cot x)+C
\int sec^2xdx = \tan x+C
\int csc^2xdx = -\cot x+C
\int \sec x\tan xdx=\sec x +C
\int \csc x\cot xdx = -\csc x +C
\int \frac{1}{\sqrt {1-x^2}}dx = \arcsin x+C
\int \frac{1}{\sqrt {a^2-x^2}}dx = \arcsin \frac{x}{a}+C
\int \frac{1}{\sqrt{a^2+x^2}}dx = \ln(x+\sqrt{a^2+x^2})+C
\int \frac{1}{\sqrt{x^2-a^2}}dx=\ln(x+\sqrt{x^2-a^2})+C
\int \frac{1}{1+x^2}dx=\arctan x+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}{x^2-a^2}dx=\frac{1}{2a}\ln \frac{x-a}{x+a}+C
\sqrt{a^2-x^2}=\frac{a^2}{2}\arcsin \frac{x}{a}+\frac{x}{2}\sqrt{a^2-x^2}+C

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