# 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:

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

Learn how to solve integrals of rational functions problems step by step online.

$\frac{1}{x\left(x+1\right)\left(2x+3\right)}=\frac{A}{x}+\frac{B}{x+1}+\frac{C}{2x+3}$

Learn how to solve integrals of rational functions problems step by step online. Integral of 1/(x(x+1)*(2x+3)) with respect to x. Rewrite the fraction \frac{1}{x\left(x+1\right)\left(2x+3\right)} in 3 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by x\left(x+1\right)\left(2x+3\right). Multiplying polynomials. Simplifying.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.49 seconds