[sin^2(x)]^2
=>[(1 -cos(2x)/2)]^2
=>1/4[1 + cos^2(2x) - 2cos(2x)]
=>1/4[1 - 2cos(2x) + (1 + cos(4x)/2 ] se usa la identidad para cos^2x
=>(1/4) - (1/2)cos(2x) + (1/8) + (1/8)cos(4x) cambio de variable para el angulo
=>(3/8) - (1/2)cos(2x) + (1/8)cos(4x)
∫sin^4(x)dx = 3/8∫dx - 1/2∫cos(2x) dx + 1/8∫cos(4x) dx
∫sin^4(x)dx = (3/8)x - (1/2)sin(2x)*(1/2) + (1/8)sin(4x)*(1/4) + c
∫sin^4(x)dx = (3/8)x - (1/4)sin(2x) + (1/32)sin(4x) + c
