令sinx=y ,則∫sinxdsinx=∫ydy= （y^2)/2所以原式=〔（sinx)^2〕/2=(1-cos2x)/4

∫x^2sin2x dx=-1/2*∫x^2 d(cos2x)

=-1/2*[x^2cos2x-∫cos2x d(x^2)]

=-1/2*[x^2cos2x-∫2xcos2x dx]

=-1/2*[x^2cos2x-∫x d(sin2x)]

=-1/2*[x^2cos2x-xsin2x+∫sin2xdx]

=-1/2*x^2cos2x+1/2*xsin2x+1/4*cos2x+C

y＝sin2x-sinx的不定積分是-2分之1乘以cos2x＋cosx＋C（C為常數）。