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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: $z=\tan\left(\frac{x}{2}\right)$

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Problems Solved

Evaluate the integral $\int_0^{2\pi}\frac{1}{cos2x-2}dx$
Evaluate the integral $\int_0^{2\pi}\left(\frac{1}{\left(2+cos\left(a\right)\right)}\right)da$
$\frac{dy}{dx}=sin\:\left(x-y+1\right)$
Evaluate the integral $\int_0^{\pi\:\:}\frac{d\theta\:\:\:}{2+\cos\:\theta\:\:\:}$
Find the integral $\int\frac{1}{1+2\cos\left(x\right)-\sin\left(x\right)}dx$
Find the integral $\int\frac{1}{cos-1}dx$
Find the integral $\int\:\frac{x^{10}}{1-sec\left(x^{11}\right)}\:dx$
Evaluate the integral $\int_0^{\frac{\pi}{2}}\left(\frac{4}{\left(1+cosx\right)^2}\right)dx$

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