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# Integrate the function $\frac{1}{\left(x-1\right)\left(x+2\right)}$ from $2$ to $5$

## Step-by-step Solution

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###  Videos

$\frac{62}{225}$
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##  Step-by-step Solution 

Problem to solve:

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Specify the solving method

1

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

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

Learn how to solve definite integrals problems step by step online.

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

Learn how to solve definite integrals problems step by step online. Integrate the function 1/((x-1)(x+2)) from 2 to 5. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x+2\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x-1\right)\left(x+2\right). Multiplying polynomials. Simplifying.

$\frac{62}{225}$

##  Explore different ways to solve this problem

SnapXam A2

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a
b
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x
y
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(◻)
+
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◻/◻
/
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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:

Definite Integrals

~ 0.39 s

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