1、∫xln（1+x）dx＝1/2*x^2*ln(x+1)-1/2∫x^2dx/(x+1)＝1/2*x^2*ln(x+1)-1/4*x^2+1/2*x-1/2*ln(x+1)+C
2、∫[1,e]sin（inx）dx＝∫[0,1]e^y*sinydy＝e^y*siny[0,1]-∫[0,1]e^y*cosydy＝e*sin1-(e^y*cosy[0,1]+∫[0,1]e^y*sinydy),∫[0,1]e^y*sinydy＝1/2*(e*sin1-e*cos1+1)
1、∫xln（1+x）dx＝1/2*x^2*ln(x+1)-1/2∫x^2dx/(x+1)＝1/2*x^2*ln(x+1)-1/4*x^2+1/2*x-1/2*ln(x+1)+C
2、∫[1,e]sin（inx）dx＝∫[0,1]e^y*sinydy＝e^y*siny[0,1]-∫[0,1]e^y*cosydy＝e*sin1-(e^y*cosy[0,1]+∫[0,1]e^y*sinydy),∫[0,1]e^y*sinydy＝1/2*(e*sin1-e*cos1+1)