∫ (sin²x - sin⁴x) dx

∫ (sin²x - sin⁴x) dx
∫ (sin²x - sin⁴x) dx

∫ (sin²x - sin⁴x) dx
∫ (sin²x - sin⁴x) dx
=∫sin²x(1-sin²x)dx
=∫sin²x·cos²x dx
=∫(sinx·cosx)²dx
=∫(½·sin2x)²dx
=1/4·∫(sin2x)²dt
=1/4·∫(1-cos4x)/2 dx
=1/8·∫(1-cos4x)dx
=1/8·(x-1/4·sin4x)+C
=x/8-1/32·sin4x+C

sin²x - sin⁴x = sin²Xcos²X = (1/4)sin²2X