Download the App!

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

Verify by differentiation that the formula is correct.

$ \displaystyle \int x\sqrt{a + bx} \,dx = \frac{2}{15b^2}(3bx - 2a)(a + bx)^{3/2} + C $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{2}{3 b^{2}}(b x-2 a) \sqrt{a+b x}+C$

03:42

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Baylor 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.

03:51

Verify by differentiation …

02:38

03:08

01:17

Determine the following in…

02:42

Find the integrals .Check …

01:08

Verify the following indef…

okay. Using the product rule weaken drive after promise acts to be too over three b squared times G prime of acts times h of acts pushed g of x times. So now that we have this recall the fact that G prime vexes B and then we know we also h promise tax. Therefore, what we have is the integral of acts over sward of a plus. P axe is to over three b square, which is this part over here you can see familiar times B X minus Julia times a plus B ox plus C.

View More Answers From This Book

Find Another Textbook