How do you find $\int cos x csc x d x$ $int cosxcscxdx$ ?

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Answer 1 · 2018-04-10T22:05:38

$\int cos x csc x d x = ln | sin x | + C$ $intcosxcscxdx=ln|sinx|+C$

Recall that $csc x = \frac{1}{sin x},$ $cscx=1/sinx,$ giving us

$\int \frac{cos x}{sin x} d x$ $intcosx/sinxdx$ .

This can be solved with a substitution.

$u = sin x$ $u=sinx$

$d u = cos x d x$ $du=cosxdx$

We then have

$\int \frac{d u}{u} = ln | u | + C$ $int(du)/u=ln|u|+C$

Rewriting in terms of $x$ $x$ yields

$\int cos x csc x d x = ln | sin x | + C$ $intcosxcscxdx=ln|sinx|+C$

How do you find ∫cosxcscxdxint cosxcscxdx ?