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Q. 78

Found in: Page 465


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.



See the step by step solution

Step by Step Solution

Step1. Given Information

The integral is as follows.


The objective is ton solve the integral.

Step2. Long division

The polynomial long division method is calculated below.

x-3x2+1x33x2+2x3x3+x 3x2+x 3x23x

The expression is in the form of x33x2+2x3x2+1=x3+xx2+1

Step3. Solution

The integral is solved below.


Therefore, the value is x223x+12lnx2+1+C.

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