# Step-by-step Solution

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
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

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

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 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}$$\,\,\left(\approx 0.2755595243948227\right)$
$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$