Question

Find the integral of the following functions with respect to x:

(a) sinx sin2x​

Answer 1

= ∫ sinx sin2x dx

= 1/2 ∫ 2sinx sin2x dx

{ 2sinAsinB = cos (A–B) – cos (A+B) }

= 1/2 ∫ cos ( 2x – x ) – cos ( 2x + x ) dx

= 1/2 ∫ ( cosx – cos3x ) dx

= 1/2 [ sinx – sin3x/3 ] + C