# Integration formulas

$\Large \int \normalsize x^n dx = \dfrac{x^{n+1}}{n+1}+C$

$\Large \int \normalsize \dfrac{1}{x} dx = \log{x}+C$

$\Large \int \normalsize a^x dx = \dfrac{a^x}{\log{a}}+C$

$\Large \int \normalsize e^x dx = e^x+C$

### Trigonometric functions

$\Large \int \normalsize \sin{x} dx = -\cos{x}+C$

$\Large \int \normalsize \cos{x} dx = \sin{x}+C$

$\Large \int \normalsize \sec^2{x} dx = \tan{x}+C$

$\Large \int \normalsize \csc^2{x} dx = -\cot{x}+C$

$\Large \int \normalsize \sec{x}\tan{x} dx = \sec{x}+C$

$\Large \int \normalsize \csc{x}\cot{x} dx = -\csc{x}+C$

### Hyperbolic functions

$\Large \int \normalsize \sinh{x} dx = \cosh{x}+C$

$\Large \int \normalsize \cosh{x} dx = \sinh{x}+C$

$\Large \int \normalsize \tanh{x} dx = \log_{e}{|\cosh{x}|}+C$

$\Large \int \normalsize \coth{x} dx = \log_{e}{|\sinh{x}|}+C$

$\Large \int \normalsize \operatorname{sech}{x} dx = 2\tan^{-1}{(e^x)}+C$

$\Large \int \normalsize \operatorname{csch}{x} dx = 2\cosh^{-1}{(e^x)}+C$

$\Large \int \normalsize \sec^2h{x} dx = \tanh{x}+C$

$\Large \int \normalsize \csc^2h{x} dx = -\cot{x}+C$

$\Large \int \normalsize \operatorname{sech}{x}\tanh{x} dx = -\operatorname{sech}{x}+C$

$\Large \int \normalsize \operatorname{csch}{x}\coth{x} dx = -\csc{x}+C$

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