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Evaluate the given integral.$$\int 4^{2 x} d x$$

$$\frac{(\ln x)^{4}}{4}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Harvey Mudd College

Baylor University

University of Nottingham

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 know that the integral of four to the U Do You is equal to four to the U over natural log of four plus c. So let's take you to be two x that way do you over to is equal to DX and we can rewrite this integral expressing it as for to the U. So this is equal to one half times the integral of four to the U, which is equal to four to the U, which is two. X all over two times Eleanor four plus C and for it is equal to two squared so we can rewrite this again as four to the two x all over four times Ellen of to plus C and that completes the problem.

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