Evaluate the indefinite integral. (Enter all trigonometrical functions in terms of sin.) ?

Question

integral of cot(8x)

Please explain.

Sin over cosine? but what do i do with the 8?

Answer 1

∫ cos(8x)/sin(8x) dx

you need to use a substitution to make this clearer

let u = sin(8x)

then du = 8 cos(8x) dx

thus the integral becomes .. . .

1/8 ∫ 1/u du

= 1/8 ln|u| + C

= (1/8) ln|sin(8x)| + C