Final answer to the problem
$\frac{1}{2}\arctan\left(\frac{\tan\left(\frac{2\pi }{2}\right)}{2}\right)- \left(\frac{1}{2}\right)\arctan\left(\frac{\tan\left(\frac{0}{2}\right)}{2}\right)$
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Step-by-step Solution
Learn how to solve integrals of rational functions of sine and cosine problems step by step online. Integrate the function 1/(5+3cos(x)) from 0 to 2*pi. We can solve the integral \int\frac{1}{5+3\cos\left(x\right)}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.
Final answer to the problem
$\frac{1}{2}\arctan\left(\frac{\tan\left(\frac{2\pi }{2}\right)}{2}\right)- \left(\frac{1}{2}\right)\arctan\left(\frac{\tan\left(\frac{0}{2}\right)}{2}\right)$
