2.设f(x)=x2lnx,由函数乘积的求导法则,(x2lnx)′=2xlnx+x,等式两边同时求区间[1,e]上的定积分,有:\int_1^e{{{({{x^2}lnx})}^'}dx}=\int_1^e{2xlnxdx}+\int_1^e{xdx}\int_1^e{{{({{x^2}lnx})}^'}dx}=\int_1^e{2xlnxdx}+\int_1^e{xdx}. ...