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

Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

1x2+432dx

Short Answer

Expert verified

The solution of the integral isx4x2+4+C.

Step by step solution

01

Step 1. Given Information.

The given integral is1x2+432dx.

02

Step 2. Solve. 

To solve the integral, let x=2sinu, so derivation of uis dx=2cosudu.

Thus, substitute u into the original integral,

role="math" localid="1648802019739" 1x2+432dx=12sinu2+4322cosudu=14sin2u+4322cosudu=14(sin2u+1)322cosudu=18sin2u+4322cosudu=141sin2u+132cosuduLet'susetheidentitysin2x+cos2x=1=141cos2u32cosudu=141cos2udu=14tanudu

03

Step 3. Solve. 

By proceeding with the calculation further, substitute back uin the above equation,

=14tansin-1x2du=x4x2+4+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