Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Calculate each of the integrals in Exercises 17–46. For some integrals you may need to use polynomial long division, partial fractions, factoring or expanding, or the method of completing the square.

16x2x2+11-2xdx

Short Answer

Expert verified

The value of integral is-2x4-43x3-5x2-5x-52ln2x-1+C.

Step by step solution

01

Step 1. Given Information.

The given integral is16x2x2+11-2xdx.

02

Step 2. Calculation.  

Rewrite the integral:

-16x2x2+12x-1dx

Perform the long division method:

-16x2x2+11-2xdx=-16x32+x24+5x8+516+5162x-1dx=-16x32dx+x24dx+5x8dx+516dx+5162x-1dx=-1612x44+14x33+58x22+516x+51612x-1dx=-2x4-43x3-5x2-5x-512x-1dx

Let u=2x-1,du=2dx

-2x4-43x3-5x2-5x-512x-1dx=-2x4-43x3-5x2-5x-521udu=-2x4-43x3-5x2-5x-52lnu+C=-2x4-43x3-5x2-5x-52ln2x-1+C

03

Step 4. Conclusion.

The value of integral is-2x4-43x3-5x2-5x-52ln2x-1+C.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free