👉 Try now NerdPal! Our new math app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium
ENG • ESP
Topics

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

Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
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

Solution

Formulas

Videos

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

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

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

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

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

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 integral of (1/(x-1)(x+2))dx from 2 to 5 using partial fractionsSolve integral of (1/(x-1)(x+2))dx from 2 to 5 using basic integralsSolve integral of (1/(x-1)(x+2))dx from 2 to 5 using u-substitutionSolve integral of (1/(x-1)(x+2))dx from 2 to 5 using integration by partsSolve integral of (1/(x-1)(x+2))dx from 2 to 5 using trigonometric substitution

Give us your feedback!

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
4
5
6
7
8
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:

Similar Problems Solved

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$

Evaluate the integral

$\int_{1}^{3}\cos\left(x\right)^2dx$

Evaluate the integral

$\int_{-5}^{5}\frac{1}{\sqrt{5-x}}dx$

Evaluate the integral

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Evaluate the integral

$\int_{2}^{4}\left(x^2+5x+6\right)dx$

Evaluate the integral

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

Evaluate the integral

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

Main topic:

Definite Integrals

Used formulas:

6. See formulas

Time to solve it:

~ 0.39 s

Related topics:

Definite IntegralsIntegral CalculusCalculusQuotient Rule of DifferentiationIntegrals by Partial Fraction ExpansionMatricesGaussian EliminationBasic Differentiation Rules

Supercharge your math learning

Use your academic email to get more benefits.
By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot password?

Supercharge your math learning

Use your academic email to get more benefits.


Register here if you don't have an account.
Forgot password?

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Including multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android app.

Join 500k+ students in problem solving.

Subscription. Cancel anytime.
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account
3-Month Special Plan
One-time payment of $2.97 USD.
Without automatic renewal.
Create an Account