# Step-by-step Solution

Go!
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## Step-by-step explanation

Problem to solve:

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

Learn how to solve definite integrals problems step by step online.

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

Learn how to solve definite integrals problems step by step online. Integrate 1/((x-1)(x+2)) from 2 to 5. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x+2\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x-1\right)\left(x+2\right). Multiplying polynomials. Simplifying.

## Final Answer

$\frac{62}{225}$$\,\,\left(\approx 0.2755595243948227\right)$
$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

### Main topic:

Definite integrals

### Time to solve it:

~ 0.09 s (SnapXam)