Tablica całek

$\int 0dx=C$

$\int 1dx=x+C$

$\int kdx=kx+C$

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C(n\ne -1)$

$\int \frac{1}{x}dx=\ln |x|+C$

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$\int \ln xdx=x\ln x-x+C$

$\int {\log }_{a}xdx=\frac{x(\ln x-1)}{\ln a}+C(a>0,a\ne 1,x>0)$

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$\int e^{x}dx=e^x+C$

$\int e^{-x}dx=-e^{-x}+C=\sinh x-\cosh x+C$

$\int e^{kx}dx=\frac{1}{k}{e}^{kx}+C$

$\int a^{x}dx=\frac{a^x}{\ln |a|}+C$

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$\int \frac{1}{1+x^2}dx=\mathrm{arctg}x+C$

$-\int \frac{1}{1+x^2}dx=\mathrm{arcctg}x+C$

$\int \frac{1}{\sqrt{1-x^2}}dx=\arcsin x+C$

$-\int \frac{1}{\sqrt{1-x^2}}dx=\arccos x+C$

$\int \frac{1}{x^2\sqrt{1-\frac{1}{x^2}}}dx=\mathrm{arcsec}x+C$

$-\int \frac{1}{x^2\sqrt{1-\frac{1}{x^2}}}dx=\mathrm{arccsc}x+C$

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$\int \sin xdx=-\cos x+C$

$\int \cos xdx=\sin x+C$

$\int \mathrm{tg}xdx=-\ln |\cos x|+C$

$\int \mathrm{ctg}xdx=\ln |\sin x|+C$

$\int \sec xdx=\ln |\sec x+\mathrm{tg}x|+C$

$\int \csc xdx=-\ln |\csc x+\mathrm{ctg}x|+C$

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$\int {\sin }^{2}xdx=\frac{1}{2}(x-\sin x\cos x)+C$

$\int {\cos }^{2}xdx=\frac{1}{2}(x+\sin x\cos x)+C$

$\int {\mathrm{tg}}^{2}xdx=\mathrm{tg}x-x+C$

$\int {\mathrm{ctg}}^{2}xdx=-\mathrm{ctg}x-x+C$

$\int {\sec }^{2}xdx=\mathrm{tg}x+C$

$\int {\csc }^{2}xdx=-\mathrm{ctg}x+C$

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$\int \sinh xdx=\cosh x+C$

$\int \cosh xdx=\sinh x+C$

$\int \mathrm{tgh}xdx=\ln |\cosh x|+C$

$\int \mathrm{ctgh}xdx=\ln |\sinh x|+C$

$\int \mathrm{sech}xdx=\mathrm{arctg}(\sinh x)+C$

$\int \mathrm{csch}xdx=\ln |\mathrm{tgh}\left(\frac{1}{2}x\right)|+C$