Evaluate the following indefinite integral

Question

Evaluate the following indefinite integral:

 

∫cos³x*sin⁶x dx

Answer 1

U-Substitution: u = sin x, du = cos x dx

 

∫ cos³ x sin⁶ x dx

 

= ∫ (1 - sin² x) cos x sin⁶ x dx

 

= ∫ (1 - u²)u⁶ du

 

= ∫ (u⁶ - u⁸) du

 

= u⁷/7 - u⁹/9 + C

 

= (sin⁷ x)/7 - (sin⁹ x)/9 + C