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

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##  Final answer to the problem

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

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

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

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

Learn how to solve problems step by step online.

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

Learn how to solve 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. Expand the integral \int\left(\frac{2}{x}+\frac{-3}{2\left(x+1\right)}+\frac{-1}{2\left(x-1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x}dx results in: 2\ln\left|x\right|. The integral \int\frac{-3}{2\left(x+1\right)}dx results in: -\frac{3}{2}\ln\left|x+1\right|.

##  Final answer to the problem

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
b
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f
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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