Question
Asked Oct 30, 2019

Use partial fraction decomposition to evaluate the integral.

∫6x2-13x+3/x2(x-3) dx

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Step 1

Refer to the question we need to find the integration using partial fraction for the provided integral as,

6x2-13x3
(x-3)
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6x2-13x3 (x-3)

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Step 2

Perform the partial fraction decomposition as,

6x2-13x+3 A B
xx-3)
C
x-3
x
LCM x (x-3)
6x2 -13x+3 Ax(x-3) B(x-3) r'c
x(x-3)
6x2-13x+3 4x(x-3)+B (x-3)+ x°c
r(x-3)
Expand the right side as
x -3
x
(x-3)
6x2-13x+3 xAx°C-3x4 +xB-3B
Collect the like terms
(A +C)+ x(-34+B) -3B
6x2-13x+3x
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6x2-13x+3 A B xx-3) C x-3 x LCM x (x-3) 6x2 -13x+3 Ax(x-3) B(x-3) r'c x(x-3) 6x2-13x+3 4x(x-3)+B (x-3)+ x°c r(x-3) Expand the right side as x -3 x (x-3) 6x2-13x+3 xAx°C-3x4 +xB-3B Collect the like terms (A +C)+ x(-34+B) -3B 6x2-13x+3x

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Step 3

From the find the coefficients by comparing ...

A+C= 6
-34 B13
-3B 3
Solving above
A = 4, B 1
1,C = 2
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A+C= 6 -34 B13 -3B 3 Solving above A = 4, B 1 1,C = 2

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Tagged in

Math

Calculus

Integration