Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Evaluate the given integral.$$\int\left(3 x^{2}+x\right) e^{4 x^{3}+2 x^{2}+1} d x$$

$$\frac{1}{4} e^{4 x^{3}+2 x^{2}+1}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Oregon State University

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.

02:05

Evaluate the integral.…

02:04

Evaluate the given integra…

03:38

0:00

04:14

02:53

if we take you to be for execute plus two x squared plus one. Then d becomes 12 x squared plus four x dx. And from here we can factor out for to get four times three x squared plus x dx. And now we can write this as 1/4 times the integral of each of the you. Where do you Over four replaces three x squared plus X dx, and this becomes 1/4 times e to the U, which is each of the four x cubed plus two x squared, plus one last seen, and that completes the problem.

View More Answers From This Book

Find Another Textbook

Numerade Educator

04:04

Find the partial derivatives with respect to (a) $x,$ (b) $y$ and (c) $z$.

01:52

Evaluate the given integral.$$\int \sqrt{2 x+1} d x$$

01:20

Find the critical points.$$f(x, y, z)=x^{2}+2 y^{2}+13 z^{2}+3 x y-5 x z…

01:45

Use the method of Lagrange multipliers to optimize $f$ as indicated, subject…

02:31

Evaluate the given integral.$$\int\left(2 x^{2}-3 x y^{3}+y^{2}+3\right)…

01:53

Evaluate the given integral and check your answer.$$\int\left(\frac{5}{x…

02:40

Evaluate the given integral.$$\int \frac{4 x^{2}-x+4}{x^{2}+1} d x$$

02:01

Find and classify, using the second partial derivative test, the critical po…

01:22

01:47

Evaluate the given integral.$$\int\left(3 x^{2}+x\right) e^{4 x^{3}+2 x^…