Evaluate the integral. {eq}\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{4 + 9 \cot x}{9 - 4 \cot x} \, \mathrm{d}x {/eq}

Question:

Evaluate the integral.

{eq}\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{4 + 9 \cot x}{9 - 4 \cot x} \, \mathrm{d}x {/eq}

Integration:

Integration by substitution method is used in many ways to solve the integrals. If the integrals are in fraction of two functions form or if the integrals are in product of two functions form, in both the case we use substitution method, the only thing to keep in mind is the one of the function should be the differential of the other function.