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)$