Question

How do you integrate `y=sinx/tanx` using the quotient rule?

Answer 1

`int sinx/tanx dx = sinx + C`

Explanation:

The quotient rule is a formula for finding the derivative of `u/v`, rather than the integral of `u/v`. There is no formula for finding integral of `u/v`

The integral you have specified can be deal with as follows;

`int sinx/tanx dx = int sinx/(sinx/cosx) dx`

`:. int sinx/tanx dx = int sinx * (cosx/sinx) dx`

`:. int sinx/tanx dx = int cosx dx`

`:. int sinx/tanx dx = sinx + C`