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Integration by Trigonometric Substitution


Definition

Trigonometric substitution is the substitution of trigonometric functions for other expressions. One may use the trigonometric identities to simplify certain integrals containing radical expressions.


Problems Solved

Evaluate the integral $\int_0^2\frac{x}{\left(1+2x^2\right)}dx$
$\left(x^2+4\right)dy=xydx$
$y'=x\sqrt{1-x^2}$
$\left(y^2+1\right)dx\:=\:\left(1+xy\right)dy$
Find the integral $\int\frac{x}{x^2-3}dx$
$xy\cdot dx+\left(1+x^2\right)\cdot dy=0$
Evaluate the integral $\int_{-\infty}^0\left(\frac{x}{x^2+1}\right)dx$
$\left(x-2y\right)dx+\left(2x+y\right)dy=0$

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Related Topics

Integrals by Partial Fraction Expansion
Trigonometric Integrals
Integration by Substitution
Integration by Parts
Tabular Integration
Weierstrass Substitution

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