# Table of integrals

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## Standard functionsEdit

• $\int a dx = ax + C$
• $\int x^n dx = \frac{x^{n+1}}{n+1} + C,n \ne -1$
• $\int f(x)g(x) dx = f(x) \int g(x) dx - \int f'(x) (\int g(x) dx) dx$ (integration by parts)

## Logarithmic and exponential functionsEdit

• $\int a^x dx = \frac{a^x}{\ln(a)} + C$
• $\int e^x dx = e^x + C$
• $\int \frac{dx}{x} = \ln|x| + C$
• $\int \ln(x) dx = x \ln (x) - x + C$
• $\int \log_a (x)dx = x\log_a x - \frac{a^x}{\ln(a)} + C$

## Trigonometric functionsEdit

• $\int \sin(x) dx = -\cos (x) + C$
• $\int \cos(x) dx = \sin (x) + C$
• $\int \tan(x) dx = -\ln | \cos(x) | + C = \ln |\sec(x)| + C$
• $\int \csc(x) dx = \ln|\tan (\frac{x}{2})| + C$
• $\int \sec(x) dx = \ln|\sec(x) + \tan (x)| + C$
• $\int \cot(x) dx = \ln|\sin(x)| + C$
• $\int \frac{dx}{\sqrt{1-x^2}} = \arcsin(x) + C$
• $\int -\frac{dx}{\sqrt{1-x^2}} = \arccos(x) + C$
• $\int \frac{dx}{1+x^2} = \arctan(x) + C$
• $\int -\frac{dx}{1+x^2} = \arccot(x) + C$
• $\int \frac{dx}{x \sqrt{x^2-1}} = \arcsec|x| + C$
• $\int -\frac{dx}{x \sqrt{x^2-1}} = \arccsc|x| + C$