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\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx

Integrate 1/((x-1)(x+2)) from 2 to 5

Answer

$\frac{62}{225}$

Step-by-step explanation

Problem

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$
1

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

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

Unlock this step-by-step solution!

Answer

$\frac{62}{225}$

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$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

4. See formulas

Time to solve it:

~ 0.82 seconds