请用分部积分法帮我求几道积分~1．∫xsin2xdx2.∫x^2Inxdx3.∫x^2cosxdx4.∫x^2arctanxdx5.∫1/(√x)arcsin√xdx
问题描述：
请用分部积分法帮我求几道积分~
1．∫xsin2xdx
2.∫x^2Inxdx
3.∫x^2cosxdx
4.∫x^2arctanxdx
5.∫1/(√x)arcsin√xdx
答
1．∫xsin2xdx = x(-0.5cos2x)-∫(-0.5cos2x)dx = -0.5xcos2x+0.5∫cos2xdx = -0.5xcos2x+0.25sin2x+C
2.∫x^2Inxdx = (1/3)x^3lnx-∫(1/3)x^3*(1/x)dx = (1/3)x^3lnx-1/3∫x^2dx = (1/3)x^3lnx-1/9x^3+C
3.∫x^2cosxdx = -x^2*sinx+∫2xsinxdx = -x^2*sinx+[2xcosx-∫2cosxdx] = -x^2*sinx+2xcosx+2sinx+C
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