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Integrals of Rational Functions of Sine and Cosine


Definition

The integrals of rational functions of sine and cosine are integrals where the integrand is a rational function composed of sines and cosines, usually in the denominator, which is not easily reducible. However, these integrals are easy to solve by applying the recommended substitution: $z=\tan\left(\frac{x}{2}\right)$


Problems Solved

Find the integral $\int\:\frac{dx}{5+4senx}dx$
Find the integral $\int\frac{1}{2sin\left(t\right)+cos\left(t\right)+5}dt$
Find the integral $\int\frac{1}{cos\left(x\right)+sin\left(x\right)+1}dx$
$\frac{dy}{dx}=\tan\left(x+y\right)$
Find the integral $\int\frac{secx}{3tgx+7}dx$
Find the integral $\int\left(\frac{1}{4-5\sin\left(x\right)}\right)dx$
Find the integral $\int\frac{dx}{1+\sin\left(x\right)+\cos\left(x\right)}$

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Related Topics

Improper Integrals
Integrals of Polynomial Functions
Integrals of Rational Functions
Integrals with Radicals
Integrals of Exponential Functions

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