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

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

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Integrals by partial fraction expansion

Used formulas:

5. See formulas

Time to solve it:

0.39 seconds