Table of Indefinite Integrals

This is a table of common antiderivatives and definite integrals for the Calculus students. Remember after each indefinite integral there is a general constant of integration (+C).

Antiderivatives

Elementary

$\int x^{n}\,dx={\frac {1}{n+1}}x^{n+1},\,n\neq -1$

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int e^x \, dx = e^x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \sin x \, dx = -\cos x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \cos x \, dx = \sin x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \tan x \, dx = - \ln \cos x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \sinh x \, dx = \cosh x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \cosh x \, dx = \sinh x }

Commonly encountered

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \ln x \, dx = x \ln x - x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int a^x \, dx = \frac{1}{\ln a} a^x }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{x^2+a^2} \, dx = \frac{1}{a} \tan^{-1} \frac{x}{a} = \frac{1}{a} \arctan \frac{x}{a} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{a^2-x^2} \, dx = \frac{1}{2} \ln \left| \frac{x+a}{x-a} \right| }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{\sqrt{a^2-x^2}} \, dx = \sin^{-1} \frac{x}{a} = \arcsin \frac{x}{a} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{\sqrt{x^2-a^2}} \, dx = \cosh^{-1} \frac{x}{a} = \ln(x+\sqrt{x^2-a^2}) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{1}{\sqrt{x^2+a^2}} \, dx = \sinh^{-1} \frac{x}{a} = \ln(x+\sqrt{x^2+a^2}) }

See also

• Integration
• Methods of integration

External links

• Integral table