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JH
Numerade Educator

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Problem 32 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_1^3 \frac{e^{\frac{3}{x}}}{x^2}\ dx $

Answer

$\frac{e^{3}-e}{3}$

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Video Transcript

Let's evaluate this inner girl by using to use up. They're probably several choices for you here that would work. For example, Let's just try one over X because if we look at do you negative one over x square D X and we see the X square down here on a DX over here. So looks like we're on the right track. So after doing this use of I'll first need a plot a minus sign that I got over here from the ISA. Then let's watch out for those limits of integration. So here X equals one. So plug it in and you get U equals one. But up here, plug it in for X U equals wonder. So that's our new upper limit. And then we have eat to the three over X dashes e to the one over X kun. So that's just here we have into the three U I guess. Yeah. Here, let me rewrite this. Make this a little easier to see. This is just e to the three times one of Rex. I should never end it that way. Let me write it this way. And that lets us, right? This is either the three you because this is just you here. And then I have d'You and recall that this negative with the deal is giving me the X squared on the bottom and then the DX up top. So go ahead and integrate this. If this three years bothering you, just do another use up here. And this will be your anti derivative plug in those that points. And then you get negative e to the one of all divided by three and then plus each of the three over three and we can go ahead and simplify this. Yeah, and that's your final answer.