为自己加油

用分部积分法求下列不定积分：
(1)∫xsinzdx；
(2)∫xe^2xdx；
(3)∫ln(x+1)dx

(1)∫xsinxdx=-∫xdcosx =-(xcosx-∫cosxdx) =-xcosx+sinx． (2)∫xe^2xdx=1/2∫xde^2x =1/2(xe^2x—∫e^2xdx) =1/2xe^2x一1/4∫e^2xd(2x) =1/2xe^2x-1/4e^2x+C． (3)∫ln(x+1)dx=xln(x+1)-∫x•1/(x+1)dx =xln(x+1)-∫[(x+1-1)/(x+1)]dz =xln(x+1)-∫[1-1/(x+1)]dx =xln(x+1)-x+ln|x+1|+C