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Evaluate the given integral.$$\int 10 x^{4} e^{3 x^{5}+7} d x$$

$$\frac{2}{3} e^{3 x^{5}+7}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Idaho State 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.

03:49

Evaluate the given integra…

00:49

Evaluate the integral.

01:18

Evaluate the integral.…

03:24

02:02

00:24

Evaluate.$$D_{x} \…

01:53

04:18

Evaluate the definite inte…

03:56

Evaluate integral

in this problem, we can take you to be three x to the fifth plus seven. That way do you DX is 15 x to the fourth which we can rewrite as d u equals do you over 15 equals X to the fourth DX. And now we can replace X to the fourth DX by do you over 15 and we can replace three X to the fifth plus seven by you. That way this inter girl becomes 10/15, which is to over three times the integral of each of the you, which is equal to two thirds times e to the three x to the fifth plus seven plus c, and that completes the problem.

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