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

$$e^{2 x^{2}}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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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integrate this function will use a use substitution and we'll also in order to apply that use substitution, we use the fact that the derivative of two X squared is for X. So this suggests for you to be two x squared that way. Do you is for X dx, which is what we wanted because now we can rewrite this as the integral of e to the U and the integral of each of the U is e to the U plus c. And now we can replace you by two x squared to get that this is e to the two x squared plus C and that completes the problem.

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