Download the App!

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

Find the general indefinite integral.

$ \displaystyle \int \sqrt{t} (t^2 + 3t + 2) \, dt $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{2}{7} t^{7 / 2}+\frac{6}{5} t^{5 / 2}+\frac{4}{3} t^{3 / 2}+C$

01:19

Frank Lin

01:04

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

University of Michigan - Ann Arbor

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.

01:13

Find the general indefinit…

02:37

Find the indefinite integr…

00:37

01:58

01:40

01:35

uh The theme in this problem is the power rule X. To the N. D. S. Which is adding one to the exponents and then dividing by your new expo or what I like to do is multiply by the reciprocal and don't forget about plus C. Because the derivative of a constant lazy river and the derivative of the thing and just wrote down needs to equal that. And this does, the only thing is make sure that this is a sum or difference of power. So as I'm looking at this, the square root of tee times, we can't do this rule until we simplify and we have T squared plus three T uh plus two. So my encouragement, as soon as first of all, don't write the square root, write it as T. To the one half hour. So then when you distribute in there, you know that you can just add your exponents. So I'm not doing the anti directive yet. Just rewriting as T. To the five house power Because that's 1/2 plus two. Uhh because when you multiply at the same base, you add the exponents and I ran out of space, but there should be A. D. T. Over here. So now I'm ready to do the anti griddle which is adding one to the exponential. Five house plus one is seven house. And that's why I don't like dividing by that new number because it looks prettier. If you multiply by the reciprocal, same thing with this T. To the five house power when you add one to it and when you multiply three By the reciprocal of two fists, you get six fists and the key to the three house power. And when you multiply two by the reciprocal of three half, so two times two thirds gives me four thirds, just like before you have to remember plus C. This is your correct answer, assuming I did all my math correct

View More Answers From This Book

Find Another Textbook

01:07

A prom ticket at Smith high school is $120 time is going to save money for t…

00:23

A pair of boots has an original price of $95. They are on sale for 35 percen…

01:11

A line is perpendicular to the line given by the equation - 8 = 2y + 3x. Wha…

01:48

Daniel needs to order some new supplies for the restaurant where he works. T…

Solve for y.9/4y - 12 = 1/4y - 4

01:09

ACemedicine is given in an amount proportional to a patient's body …

A certain medicine is given in an amount proportional to a patient's bo…

00:55

Jon invests $4,100 into an account that pays 5 percent simple interest each …

01:50

For a given function ƒ(x), the translation ƒ(x – 2) + 3 means the function w…

The Schwartz family spent a total of $111.75 for Internet service for 3 mont…