Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Calculus AB Resources

45 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Calculus AB but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Calculus AB flashcards! Our Calculus AB flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Calculus AB flashcards.

Flashcards: Use Substitution and Integration

Use a change of variable (aka a u-substitution) to evaluate the integral,

$\int x\sqrt{1+x^2}dx$

$\frac{1}{6}(2x+1)^{\frac{2}{3}}+C$

$\frac{1}{6}(x^2+1)^{\frac{2}{3}}+\sqrt{x}+C$

$\frac{1}{3}(x^2+1)^{\frac{3}{2}}+C$

$\frac{1}{3}x^{\frac{3}{2}}+C$

$\frac{3}{4}(x^2+1)^{\frac{3}{2}}+C$

Report an Error Copyright Notice

Flashcards: Use Substitution and Integration

Use a change of variable (aka a u-substitution) to evaluate the integral,

$\int x\sqrt{1+x^2}dx$

Your answer:

$\frac{1}{6}(2x+1)^{\frac{2}{3}}+C$

Your answer:

$\frac{1}{6}(x^2+1)^{\frac{2}{3}}+\sqrt{x}+C$

Your answer:

$\frac{1}{3}x^{\frac{3}{2}}+C$

Your answer:

$\frac{3}{4}(x^2+1)^{\frac{3}{2}}+C$

Correct answer:

$\frac{1}{3}(x^2+1)^{\frac{3}{2}}+C$

Explanation:

$\int x\sqrt{1+x^2}dx$

Integrals such as this are seen very commonly in introductory calculus courses. It is often useful to look for patterns such as the fact that the polynomial under the radical in our example, 1+x^2 , happens to be one order higher than the factor outside the radical, You know that if you take a derivative of a second order polynomial you will get a first order polynomial, so let's define the variable:

u = 1+x^2 (1)

Now differentiate with respect to to write the differential for ,

du = 2x dx (2)

Looking at equation (2), we can solve for xdx , to obtain $xdx =\frac{1}{2}du$ . Now if we look at the original integral we can rewrite in terms of

$\int x\sqrt{1+x^2}dx = \int\sqrt{1+x^2}\underbrace{xdx} = \int\sqrt{u}\left(\frac{1}{2}du \right )$

Now proceed with the integration with respect to .

$\int\sqrt{u}\left(\frac{1}{2}du \right ) = \frac{1}{2}\int u^{\frac{1}{2}}du$

$= \frac{1}{2}\left[\frac{1}{\frac{1}{2}+1}u^{\frac{1}{2}+1} \right ]+C$

$=\frac{1}{2} \left(\frac{2}{3}u^{\frac{3}{2}} \right )+C$

$=\frac{1}{3}u^{\frac{3}{2}}+C$

Now write the result in terms of using equation (1), we conclude,

$\int x\sqrt{1+x^2}dx=\frac{1}{3}(x^2+1)^{\frac{3}{2}}+C$

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

View Tutors

Salinah
Certified Tutor

SUNY at Purchase College, Bachelor of Science, Biology, General.

View Tutors

Joaquim
Certified Tutor

Ohio Wesleyan University, Bachelor of Science, Biomedical Engineering.

View Tutors

Cassandra
Certified Tutor

University of Virginia-Main Campus, Bachelor in Arts, English.

Popular Subjects

LSAT Tutors in Philadelphia, GRE Tutors in Philadelphia, SAT Tutors in Los Angeles, SAT Tutors in Houston, MCAT Tutors in Chicago, ISEE Tutors in Boston, Chemistry Tutors in Phoenix, Calculus Tutors in Phoenix, GMAT Tutors in Denver, ISEE Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Seattle, ACT Courses & Classes in San Diego, ACT Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, GRE Courses & Classes in Los Angeles, SAT Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Houston, SSAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Los Angeles, SAT Test Prep in Boston, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in Atlanta, SAT Test Prep in Chicago, GMAT Test Prep in Washington DC, SAT Test Prep in Seattle, MCAT Test Prep in Boston, SSAT Test Prep in Seattle, SSAT Test Prep in Phoenix

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Calculus AB Resources

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All Calculus AB Resources

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Flashcards: Use Substitution and Integration

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: