Question

Evaluate ∫ cos⁵x/sinx dx

\(\int\frac{cos^5x}{sinx}\)dx

Answer 1

∫ cos⁵x/sinx dx

To solve this type of integration we have to,

let cosx either sinx = t then manuplate them 

Let sin x =t then cosx dx = dt 

Also apply the formula of,

(sin²t + cos²t = 1)

= log |t| + t⁴/4 - t²

= log |sin x| + sin⁴x/4 - sin²x  (By putting t = sin x)