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

Construct examples of the thing(s) described in the following.

(a) Five integrals that can be solved with the method of

integration by substitution.

(b) Five integrals that cannot be solved with the method

of integration by substitution.

(c) Three relatively simple integrals that we cannot solve

with any of the methods we now know.

Short Answer

Expert verified

(a)

1.โˆซx7(x8โˆ’5)4dx2.โˆซexdxex+73.โˆซ(logโกx)5dxx4.โˆซtanโˆ’1โกxdx1+x25.โˆซdxx(x3โˆ’1)

(b)

1.โˆซx2+4dx2.โˆซ2x+3x2โˆ’5x+6dx3.โˆซxlogโกxdx4.โˆซex(1xโˆ’1x2)dx5.โˆซdxsinโกx+cosโกx

(c)

1.โˆซtanโกxdx2.โˆซ1x2โˆ’5x+6dx3.โˆซx2exdx

Step by step solution

01

Part (a) Step 1: List five integrals that can solve by using the substitution method

1.โˆซx7(x8โˆ’5)4dx2.โˆซexdxex+73.โˆซ(logโกx)5dxx4.โˆซtanโˆ’1โกxdx1+x25.โˆซdxx(x3โˆ’1)

02

Part (b) Step 2: List five integrals that can not be solved by substitution method

1.โˆซx2+4dx2.โˆซ2x+3x2โˆ’5x+6dx3.โˆซxlogโกxdx4.โˆซex(1xโˆ’1x2)dx5.โˆซdxsinโกx+cosโกx

03

Part (c) Step 3: List three integrals that different from part (a) and part (b)

1.โˆซtanโกxdx2.โˆซ1x2โˆ’5x+6dx3.โˆซx2exdx

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