How do you use substitution to integrate $cos x/sin x dx$ ?

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Answer 1 · 2015-07-29T17:21:16

The procedure is outlined below.

We have to evaluate, $int Cos x/Sin x * dx$

So, let $Sin x = t$
$implies Cos x*dx = dt$ (By simple differentiation)

Thus the integral $int Cos x/Sin x *dx = int dt/t$
$= Ln t + C$

In terms of $x$ , the integral is,

$int Cos x/Sin x * dx = Ln (Sin x) + C$ , where $C$ is the integration constant.

How do you use substitution to integrate cos x/sin x dxcos x/sin x dx?