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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 7.P, Problem 13P
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Chapter
Section
Problem 1P
Problem 2P
Problem 3P
Problem 4P
Problem 5P
Problem 6P
Problem 7P
Problem 8P
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Problem 10P
Problem 11P
Problem 12P
Problem 13P
Problem 14P
Problem 15P
Problem 16P
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
1 views

Evaluate ∫ − 1 ∞ ( x 4 1 + x 6 ) 2 d x .

To determine

To Find: ∫−1∞(x41+x6)2dx

Explanation

Given ∫−1∞(x41+x6)2dx=∫−1∞x8(1+x6)2dx

Let x3=u, then 3x2dx=du

When x=−1,u=−1

When x=∞,u=∞

Therefore

∫−1∞(x41+x6)2dx=13∫−1∞u2(1+u2)2 du=13∫−1∞(u2+1)−1(1+u2)2 du=13∫−1∞[11+u2−1(1+u2)2] du=13∫−1∞[11+u2] du−13∫−1∞[1(1+u2)2] du

From table of integral we have

∫1(au2+b)n du=2n−32b(n−1)∫du(au2+b)n−1+u2b(n−1)(au2+b)n−1

Using the formula, we get

∫du(u2+1)2=12∫du(u2+1)+u2(

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