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Weierstrass Substitution


Definition

In integral calculus, the Weierstrass substitution or tangent half angle substitution is a method for solving integrals, which converts a rational expression of trigonometric functions into an algebraic rational function, which can be easier to integrate. The Weierstrass substitution is very useful for integrals that involve a simple rational expression with sine and/or cosine in the denominator.


Problems Solved

Find the integral $\int\left(\frac{1}{1+sin\left(x\right)+cos\left(x\right)}\right)dx$
$y'=\sin\:\left(x-y+1\right)$
Find the integral $\int\:\frac{dx}{1-sinx}$
Find the integral $\int\left(\frac{1}{3+2\sin\left(x\right)+\cos\left(x\right)}\right)dx$
$y^'=sen^2\left(x+y-1\right)$
Find the integral $\int\frac{1}{3+5\cos\left(x\right)}dx$
$y'=\sin\left(x-y+1\right)$
$\frac{dy}{dx}=\sin\left(x+y\right)^2$

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Related Topics

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

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