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CalculusCalculus10th Edition

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Chapter 8, Problem 54RE
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Solutions

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Problem 5RE
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Problem 7RE
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Problem 10RE
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Problem 13RE
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Problem 37RE
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Problem 53RE
Problem 54RE
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Problem 79RE
Problem 80RE
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Problem 82RE
Problem 83RE
Problem 84RE
Problem 85RE
Problem 86RE
Problem 87RE
Problem 88RE
Problem 89RE
Problem 90RE
Problem 91RE
Problem 1PS
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Problem 4PS
Problem 5PS
Problem 6PS
Problem 7PS
Problem 8PS
Problem 9PS
Problem 10PS
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Problem 13PS
Problem 14PS
Problem 15PS
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Problem 17PS
Problem 18PS
Problem 19PS
Problem 20PS
Problem 21PS
Problem 22PS
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Finding an Indefinite Integral In Exercises 57-64, find the indefinite integral using any method.

∫ 3 x 3 + 4 x ( x 2 + 1 ) 2 d x

To determine

To calculate: The value of the indefinite integral ∫3x3+4x(x2+1)2dx.

Explanation

Given: We are given with the IndefiniteIntegral ∫3x3+4x(x2+1)2dx.

Formula used:

∫1ada=lna

Calculation:

Let,

I=∫3x3+4x(x2+1)2dx

I=∫x(3x2+4)(x2+1)2dx Replace x2=t

On differentiating both sides,

2xdx=dt

On substituting, we get that :

I=12∫(3t+4)(t+1)2dt=32∫t(t+1)2dt+2∫dt(t+1)2=I1−2t+1+C

Therefore

I1=32∫t

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P-15RECh-8 P-16RECh-8 P-17RECh-8 P-18RECh-8 P-19RECh-8 P-20RECh-8 P-21RECh-8 P-22RECh-8 P-23RECh-8 P-24RECh-8 P-25RECh-8 P-26RECh-8 P-27RECh-8 P-28RECh-8 P-29RECh-8 P-30RECh-8 P-31RECh-8 P-32RECh-8 P-33RECh-8 P-34RECh-8 P-35RECh-8 P-36RECh-8 P-37RECh-8 P-38RECh-8 P-39RECh-8 P-40RECh-8 P-41RECh-8 P-42RECh-8 P-43RECh-8 P-44RECh-8 P-45RECh-8 P-46RECh-8 P-47RECh-8 P-48RECh-8 P-49RECh-8 P-50RECh-8 P-51RECh-8 P-52RECh-8 P-53RECh-8 P-54RECh-8 P-55RECh-8 P-56RECh-8 P-57RECh-8 P-58RECh-8 P-59RECh-8 P-60RECh-8 P-61RECh-8 P-62RECh-8 P-63RECh-8 P-64RECh-8 P-65RECh-8 P-66RECh-8 P-67RECh-8 P-68RECh-8 P-69RECh-8 P-70RECh-8 P-71RECh-8 P-72RECh-8 P-73RECh-8 P-74RECh-8 P-75RECh-8 P-76RECh-8 P-77RECh-8 P-78RECh-8 P-79RECh-8 P-80RECh-8 P-81RECh-8 P-82RECh-8 P-83RECh-8 P-84RECh-8 P-85RECh-8 P-86RECh-8 P-87RECh-8 P-88RECh-8 P-89RECh-8 P-90RECh-8 P-91RECh-8 P-1PSCh-8 P-2PSCh-8 P-3PSCh-8 P-4PSCh-8 P-5PSCh-8 P-6PSCh-8 P-7PSCh-8 P-8PSCh-8 P-9PSCh-8 P-10PSCh-8 P-11PSCh-8 P-12PSCh-8 P-13PSCh-8 P-14PSCh-8 P-15PSCh-8 P-16PSCh-8 P-17PSCh-8 P-18PSCh-8 P-19PSCh-8 P-20PSCh-8 P-21PSCh-8 P-22PS

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