2x dx ( + 1)2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 31E
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The integrals converge. Evaluate the integrals without using tables 

2x dx
( + 1)2
Transcribed Image Text:2x dx ( + 1)2
Expert Solution
Step 1

Consider the following integral:

I=-2xx2+12dx

Substitute x2+1=t2xdx=dt in the above integral:

I=-1t2dt=-t-2dt=t-2+1-2+1-=-t-1-=-1t-

Step 2

Resubstitute t=x2+1 in I:

I=-1x2+1-=0

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