此题不易直接求积分,但可用级数展开法求
e^x=1+x+x^2/2!+x^3/3!+x^4/4!+...
(e^x)/x^2=1/x^2+1/x+1/2!+x/3!+x^2/4!+...
∫[(e^x)/x^2]dx=∫[1/x^2+1/x+1/2!+x/3!+x^2/4!+...]dx
=-1/x+lnx+x/2!+x^2/(2*3!)+x^3/(3*4!)+...
此题不易直接求积分,但可用级数展开法求
e^x=1+x+x^2/2!+x^3/3!+x^4/4!+...
(e^x)/x^2=1/x^2+1/x+1/2!+x/3!+x^2/4!+...
∫[(e^x)/x^2]dx=∫[1/x^2+1/x+1/2!+x/3!+x^2/4!+...]dx
=-1/x+lnx+x/2!+x^2/(2*3!)+x^3/(3*4!)+...