Use partial fractions to evaluat ∫dx/x(x2 + 1)2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 53E
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Use partial fractions to evaluat ∫dx/x(x2 + 1)2

Expert Solution
Step 1

Given,

The integral is,

              Calculus homework question answer, step 1, image 1

Calculus homework question answer, step 1, image 2

Differentiate both the sides with respect to x,

Calculus homework question answer, step 1, image 3

 

Step 2

The form of the partial decomposition is

Calculus homework question answer, step 2, image 1

By choosing the values of u,

Plug u = 1

Calculus homework question answer, step 2, image 2

Now, plug u = 0,

Calculus homework question answer, step 2, image 3

By plugging the values of A and C in the above expression,

B = -1

So, the required expression becomes,

Calculus homework question answer, step 2, image 4

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