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Step-by-step Solution

Integrate $\frac{1}{\left(x-1\right)\left(x+2\right)}$ from $2$ to $5$

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Answer

$\frac{62}{225}$$\,\,\left(Decimal: 0.2755595243948227\right)$

Step-by-step explanation

Problem to solve:

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$
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Rewrite the fraction $\frac{1}{\left(x-1\right)\left(x+2\right)}$ in $2$ simpler fractions using partial fraction decomposition

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

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Answer

$\frac{62}{225}$$\,\,\left(Decimal: 0.2755595243948227\right)$

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