Question

Give the Integration of
sin^4x

Answer 1

∫sin⁴x dx

= ∫(sin²x)² dx

= ∫{(1 - cos 2x)/2}² dx

= 1/4 ∫(1 - cos 2x)² dx

= 1/4 ∫ (1+cos² 2x - 2 cox 2x) dx

= 1/4 [x - sin 2x + x/2+ (sin 4x)/8 ]  + c

I hope it helps you ^_^