Question

Integral dari sin^4 x ?

Answer 1

Cos 2x = 1 - 2sin²x
sin²x = (1/2)(1 - cos 2x)

maka:
int (sin x)⁴ dx = int (sin² x)² dx
= int (1/4 (1 - cos 2x)²) dx
= 1/4 int (1 - 2 cos 2x + cos² 2x) dx
= 1/4 (x - sin 2x + (1/8)(4x + sin 4x)) + c