## anonymous one year ago This is probably the wrong section but: How does one find the integral of csc^10(x)cot(x)dx?

1. phi

csc x = (sin x)^-1 $\frac{d}{dx} \csc x = \frac{d}{dx} (\sin x)^{-1}=-( \sin x)^{-2} \cos x = - \frac{1}{\sin x} \frac{\cos x }{\sin x}= - \csc x \cot x$ let u = csc x so that $$du = - \csc x \cot x\ dx$$ and $\int \csc^{10}(x) \cot(x)\ dx =- \int \csc^{9}(x) (- \csc x\cot(x))\ dx \\ =- \int u^9 du$

2. anonymous

Thank you!