1 Answers

Best Answer

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)