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

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

Answer

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

Step-by-step explanation

Problem

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

Using partial fraction decomposition, the fraction $\frac{1}{\left(2+x\right)\left(1+x\right)}$ can be rewritten as

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

Unlock this step-by-step solution!

Answer

$\ln\left|\frac{1+x}{2+x}\right|+C_0$
$\int\frac{1}{\left(x+1\right)\left(x+2\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

3. See formulas

Time to solve it:

0.81 seconds