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Step-by-step Solution

Integral of $\frac{1}{\left(x+2\right)\left(x-3\right)}$ with respect to $x$

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Answer

$-\frac{1}{5}\ln\left|x+2\right|+\frac{1}{5}\ln\left|x-3\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\left(x+2\right)\left(x-3\right)}dx$
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Rewrite the fraction $\frac{1}{\left(x+2\right)\left(x-3\right)}$ in $2$ simpler fractions using partial fraction decomposition

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

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Answer

$-\frac{1}{5}\ln\left|x+2\right|+\frac{1}{5}\ln\left|x-3\right|+C_0$

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