∫ xsin^4x dx = ∫ x(sin²x)² dx= ∫ x[1/2 • (1 - cos2x)]² dx= (1/4)∫ x(1 - 2cos2x + cos²2x) dx= (1/4)∫ x dx - (1/2)∫ xcos2x dx + (1/8)∫ (x + xcos4x) dx= (3/8)∫ x dx - (1...