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# Find the integral $\int\frac{x-2}{x\left(x+1\right)\left(x-1\right)}dx$

## Step-by-step Solution

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###  Videos

$2\ln\left(x\right)-\frac{3}{2}\ln\left(x+1\right)-\frac{1}{2}\ln\left(x-1\right)+C_0$
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##  Step-by-step Solution 

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Rewrite the fraction $\frac{x-2}{x\left(x+1\right)\left(x-1\right)}$ in $3$ simpler fractions using partial fraction decomposition

$\frac{x-2}{x\left(x+1\right)\left(x-1\right)}=\frac{A}{x}+\frac{B}{x+1}+\frac{C}{x-1}$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\frac{x-2}{x\left(x+1\right)\left(x-1\right)}=\frac{A}{x}+\frac{B}{x+1}+\frac{C}{x-1}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x-2)/(x(x+1)(x-1)))dx. Rewrite the fraction \frac{x-2}{x\left(x+1\right)\left(x-1\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by x\left(x+1\right)\left(x-1\right). Multiplying polynomials. Simplifying.

$2\ln\left(x\right)-\frac{3}{2}\ln\left(x+1\right)-\frac{1}{2}\ln\left(x-1\right)+C_0$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

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