∫（xsin x）²dx 不定积分怎么求

∫（xsin x）²dx 不定积分怎么求
∫（xsin x）²dx 不定积分怎么求

∫（xsin x）²dx 不定积分怎么求
∫（xsin x）²dx
=Sx^2*(sinx)^2 dx
=Sx^2*(1-cos2x)/2 dx
=1/2*Sx^2dx-1/2*Sx^2 cos2x dx
=1/6*x^3-1/4*Sx^2dsin2x
=1/6*x^3-1/4*x^2sin2x+1/4*Ssin2xdx^2
=1/6*x^3-1/4*x^2sin2x+1/2*Sxsin2xdx
=1/6*x^3-1/4*x^2sin2x-1/4*Sxdcos2x
=1/6*x^3-1/4*x^2sin2x-1/4*xcos2x+1/4*Scos2xdx
=1/6*x^3-1/4*x^2sin2x-1/4*xcos2x+1/8*sin2x+c