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Evaluate the given integral.$$\int x^{3} e^{4 x} d x$$

$$\frac{1}{128}\left(32 x^{3}-24 x^{2}+12 x-3\right) e^{4 x}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 9

Two Integration Techniques

Integrals

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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.

01:13

Evaluate the given integra…

02:32

Evaluate the integral.…

03:40

Evaluate the integral.

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00:56

evaluate the following int…

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Evaluate the following int…

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04:54

01:10

the derivative of four X Cubed is 12 ax squared. So let's take you to be for X cubed that way, do you? Is 12 ax squared and we can divide through by 12 to get d you over 12 is X squared DX, and now we can write this as 1/12 times the integral of e to the U. We know that the integral of each of the U is each of you plus C. So this is equal to 1 12 times he times e to the U, which is e to the four x cubed. And finally we have plus C and that completes the problem.

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