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Evaluate the definite integral.

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

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01:18

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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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

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