∵∫(sinx)^4dx=∫[(1-cos(2x))/2]²dx
=∫[(1-2cos(2x)+cos²(2x))/4]dx
=∫[(1-2cos(2x)+(1+cos(4x))/2)/4]dx
=∫[3/8-cos(2x)/2+cos(4x)/8]dx
=3x/8-sin(2x)/4+sin(4x)/32+C (C是积分常数)
∴3x/8-sin(2x)/4+sin(4x)/32+C (C是积分常数)的导数是sinx的4次方.