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Integrate each of the given functions.$$\int \frac{12 x^{2}-4 x-2}{4 x^{3}-x} d x$$

$2 \ln |x|+\frac{3}{2} \ln |2 x+1|+\frac{1}{2} \ln |2 x-1|+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 9

Integration by Partial Fractions: Nonrepeated Linear Factors

Integrals

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University of Nottingham

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Evaluate each definite int…

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in the problem we have indication. 12 X. Quiet -4 X -2 upon four XQ -X. Index. Mhm. No this can't be represented us. 12 X Squire -4 X -2. Phone X into two x plus one and 2. two X -1. Or this is A upon X. Class be upon. Do you explain us 1? Let's see upon two X- Man. No. To find the village of abc. So this is Develop Squire -4 X -2 equals into two x plus one In the two X -1 plus bx into two x -1 plus six. Into do explainable. No the value of A is equal to two B equals three and C is equal to -1. Therefore the integration become Diggle two upon X plus three upon two x plus one. My husband upon two x plus one. The X There four days twice a landmark. X Plus 3.2. Ellen Mod two weeks plus one minus half. Ellen Mod two X -1 Plus C. Or further after taking half as common. This is for L. N more X Plus three. Ln mud two x plus 1 -1 Ellen Mod two X -1. Let's see now here this is equal to half and then extra. The power fall plus Ln two weeks plus one. to the power three minus Ln two x -1 plus the this is equal to half into Ellen mod export food into two X -1. This is plus one to the power three upon two X -1. Let's see. So for all we have answered us half Ellen actually, Power fall into two X plus one to the Power three divided by To explain this one plus C. So this is the overall answer.

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