求xe^xdx\(e^x-1）^2的不定积分
问题描述：
求xe^xdx\(e^x-1）^2的不定积分
答
令a=e^xx=lnadx=da/a原式=∫alna*(da/a)/(a-1)^2=∫lnada/(a-1)^2=∫lnad[-1/(a-1)]=lna[-1/(a-1)]-∫[-1/(a-1)]dlna=-lna/(a-1)+∫[1/a(a-1)]da=-lna/(a-1)+∫[da/a-da/(a-1)]=-lna/(a-1)+lna-ln|a-1|+C=-x/(e^x-1)...