请用分部积分法帮我求几道积分~

显示全部楼层 · 2009-4-3 18:00:55

1．∫xsin2xdx
2. ∫x^2Inxdx
3. ∫x^2cosxdx
4. ∫x^2arctanxdx
5. ∫1/(√x)arcsin√xdx
要步骤呀~
ElfJerry：谢谢你的回答！我的邮箱：[email protected]，麻烦发步骤给我呀~

千问 · 2009-4-3 18:00:55

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 我到点上课了。这样吧，放学回家后把做题步骤照个照片发给你...