Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of 1/((x+1)(x+2))

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

Answer

$\ln\left|x+1\right|-\ln\left|x+2\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\left(x+1\right)\left(x+2\right)}dx$
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 of the unknown coefficients. The first step is to multiply both sides of the equation by $\left(x+1\right)\left(x+2\right)$

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

Unlock this step-by-step solution!

Answer

$\ln\left|x+1\right|-\ln\left|x+2\right|+C_0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

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

Main topic:

Integrals by partial fraction expansion

Used formulas:

5. See formulas

Time to solve it:

~ 0.77 seconds