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Evaluate the given integral.$$\int 2 x\left(5^{4 x^{2}}\right) d x$$

$$\frac{5^{4 x^{2}}}{4 \ln 5}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Oregon State University

Baylor University

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.

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Evaluate the integral.…

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Evaluate the definite inte…

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Evaluate the given integra…

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the derivative of four X squared is a X, and we know how to integrate five to the U. So let's take you to be for X squared that way. Do you? Is equal to eight x dx, which means that do you over eight is equal to X DX and this becomes to over eight, which is 1/4 times the integral of five to the year, which is equal to 1/4 times five to the U all over Eleanor five plus C, which is equal to five to the four x squared all over four times Ellen of five plus C and that completes the problem.

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