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Evaluate the given integral.$$\int \frac{e^{\frac{-3}{x}}}{x^{2}} d x$$

$$\frac{1}{3} e^{\frac{1}{x}}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Campbell University

Baylor University

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.

04:54

Evaluate the integral.

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Evaluate the integral.…

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02:04

Evaluate the given integra…

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01:13

03:17

Evaluate the integrals.

05:32

if we let you equal minus three over X, we get dear is equal to three over X squared DX. And if we divide through by three, we get do you over three is equal to one over x squared DX and this allows us to remove one over X squared d X and rewrite this integral in terms of you. So this becomes one third times the integral of eats of the you. Do you? And we know that the integral of each of you is each of you plus C. So this is equal to one third times E to the U, which is minus three over X plus c, and that completes the problem.

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