Evaluate the integral (natural log)

Question

∫(1 to 2)e^1/x/x²(dx)

Answer 1

Use u=¹/x so u = -¹/_x²

and the bounds are u(1)=1 and u(2)=¹/₂= 0.5,

∫₁²e^1/x/x²(dx) = ∫₁^0.5e^u(-du)=∫_0.5¹e^u(du) = e^u|_0.5¹ = e-√e