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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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Solution

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Final Answer

$\frac{62}{225}$
Got another answer? Verify it here!

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

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

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 $\left(x-1\right)\left(x+2\right)$

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

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

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

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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.

Final Answer

$\frac{62}{225}$

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

Solve int(1/((x-1)(x+2)))dx&2&5 using partial fractionsSolve int(1/((x-1)(x+2)))dx&2&5 using basic integralsSolve int(1/((x-1)(x+2)))dx&2&5 using u-substitutionSolve int(1/((x-1)(x+2)))dx&2&5 using integration by partsSolve int(1/((x-1)(x+2)))dx&2&5 using trigonometric substitution
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7
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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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

Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.1 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegrals by Partial Fraction ExpansionMatricesGaussian Elimination

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