Question

integral of x^5 cosec^2(x)^6 dx​

Answer 1

Step-by-step explanation:

We have,

$\int {x}^{5} \cosec^{2} ( {x}^{6} ) dx$

$let \: \: {x}^{6} = \alpha \\ \implies6 {x}^{5} dx = d \alpha \\ \implies {x}^{5} dx = \frac{d \alpha }{6}$

$= \int \cosec^{2} ( \alpha ) \frac{d \alpha }{6}$

$= \frac{1}{6} \int \cosec^{2} ( \alpha )d \alpha$

$= - \frac{1}{6} \cot( \alpha ) + c$

$= - \frac{1}{6} \cot( {x}^{6} ) + c$