# How do I evaluate the indefinite integral intsin(x)/(cos^3(x))dx ?

Jul 30, 2014

$= \frac{1}{2} \cdot \frac{1}{{\cos}^{2} \left(x\right)} + c$, where $c$ is a constant

Explanation

$= \int \sin \frac{x}{{\cos}^{3} \left(x\right)} \mathrm{dx}$

let's assume $\cos \left(x\right) = t$, $\implies$ $- \sin \left(x\right) \mathrm{dx} = \mathrm{dt}$

$= \int - \frac{\mathrm{dt}}{t} ^ 3$

$= - \int {t}^{-} 3 \mathrm{dt}$

$= - {t}^{-} \frac{2}{- 2} + c$, where $c$ is a constant

substituting back the value of $t$,

$= \frac{1}{2} \cdot \frac{1}{{\cos}^{2} \left(x\right)} + c$, where $c$ is a constant