# Step-by-step Solution

## Find the integral $\int\frac{1}{x\left(x+1\right)}dx$

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### Videos

$\ln\left(x\right)-\ln\left(x+1\right)+C_0$

## Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

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

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

Learn how to solve integrals by partial fraction expansion problems step by step online.

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

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(1/(x(x+1)))dx. Rewrite the fraction \frac{1}{x\left(x+1\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 x\left(x+1\right). Multiplying polynomials. Simplifying.

$\ln\left(x\right)-\ln\left(x+1\right)+C_0$
SnapXam A2

### beta Got another 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
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

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

### Main topic:

Integrals by Partial Fraction expansion

~ 0.33 s