Question

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

Answer 1

The procedure is outlined below.

Explanation:

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.