# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

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

$\begin{matrix}\left(-1\right)\left(-5\right)=5\\ \left(-1\right)+\left(-5\right)=-6\end{matrix}$

Learn how to solve definite integrals problems step by step online. Integrate 1/(x^2-6x+5) from 2 to 4. Factor the trinomial x^2-6x+5 finding two numbers that multiply to form 5 and added form -6. Thus. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x-5\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-5\right).

$-0.5493$
$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$