Question

If `int(sin2x)/(sin5x  sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = ______

Options

• sin 5x

• sin 4x

• sin 2x

• sin 6x

Answer 1

If `int(sin2x)/(sin5x  sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = sin 5x.

Explanation:

`int(sin2x)/(sin5x  sin3x)dx`

= `int(sin(5x - 3x))/(sin5x sin3x)dx`

= `int(sin5x cos3x - cos5x sin3x)/(sin5x sin3x)dx`

= `int(cot3x - cot5x)`dx

= `1/3log|sin 3x| - 1/5log|sin 5x| + c`