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Problem 69 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^{e^4}_{e} \frac{dx}{x \sqrt{\ln x}} $

Answer

$2$

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Video Transcript

we can consider Are you to be natural of acts, Which means that our d axe is simply axe d'you. Okay, this now means that our limits of integration change. Our bottom limit is gonna be natural. Lot of E, which is simply one in our top limit, is gonna be natural lot of each of the fourth, which is simply for because remember, Ellen, times e just has one. It just cancels out, Okay, Now we're gonna be using the power will, which means we increased the exported by one. And then we divide by the new expert. So from negative 1/2 which is the same thing as one over scored of you, the expensive 1/2 we add one and we end up with positive 1/2 defined by the exponents. Now, using the fundamental dear. My calculus, we can pull again. We end up with two