int_(1)^(2)(e^(1/x))/(x^(2))dx Substitute (1)/(x)=u And -(dx)/(x^(2))=du Limits of Integration will change from int_(1)^(2) to int_(1/1)^(1/2)=int_(1)^(1/2) =-int_(1)^(2)e^(1/x)(-(dx)/(x^(2))) =-int_(1)^(1/2)e^(u)du Remember that int_(a)^(b)f(x)dx=-int_(b)^(a)f(x)dx -int_(1/2)^(1)e^(u)du=[e^(u)]_(1/2)^(1)=e^(1)-e^(1/2)=e-sqrt(e) Result: int_(1)^(2)(e^(1/x))/(x^(2))dx=e-sqrt(e)