求不定积分?∫ ln(x+1) dx
问题描述：
求不定积分?∫ ln(x+1) dx
答
=xln(x+1)-x/(x+1)dx=xln(x+1)-x+1/(X+1)dx=xln(x+1)-x+ln(x+1)
答
分部积分
∫ln(x+1)dx
=xln(x+1)-∫xd[ln(x+1)]
=xln(x+1)-∫[x/(x+1)]dx
=xln(x+1)-∫[1-1/(x+1)]dx
=xln(x+1)-∫dx+∫[1/(x+1)]d(x+1)
=xln(x+1)-x+ln(x+1)+C
答
∫ln(x+1)dx=∫ln(x+1)d(x+1)=(ln(x+1))(x+1)-∫(x+1) d(ln(x+1))
=(x+1)ln(x+1)-∫((x+1)/(x+1))dx=(x+1)ln(x+1)-x+c