XSMath

Mathematics and Statistics Resources

Integration

Properties

$\int_{a}^b cdx=c(b-a)$

$\int_{a}^b cf(x)dx=c\int_{a}^b f(x)dx$

$\int_{a}^b [f(x)+g(x)]dx=\int_{a}^b f(x)dx+\int_{a}^b g(x)dx$

$\int_{a}^b [f(x)-g(x)]dx=\int_{a}^b f(x)dx-\int_{a}^b g(x)dx$

Indefinite Integrals

$\int kdx=kx + C$

$\int x^ndx=\frac{x^{n+1}}{n+1} + C$ $n\neq-1$

$\int \frac{1}{x}dx=ln|x| + C$ $x\neq0$

$\int e^xdx=e^x + C$

$\int e^{ax}dx=\frac{1}{a}e^{ax} + C$

$\int b^xdx=\frac{b^x}{lnb} + C$

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

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

$\int \sec^2xdx=\tan x + C$

$\int \csc^2xdx=-\cot x + C$

$\int \sec x\tan xdx=\sec x + C$

$\int \csc x\cot xdx=-\csc x + C$

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

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

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

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

Video Links

Integration by Substitution

Integration by Parts

Integration by Parts Definite Integrals

Integration by Partial Fractions