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Step-by-step Solution

Integrate $\frac{1}{x^2-6x+5}$ from $2$ to $4$

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Answer

$-\frac{7}{\sqrt[3]{3}}$$\,\,\left(Decimal: -0.5493061443340549\right)$

Step-by-step explanation

Problem to solve:

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$
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Factor the trinomial $x^2-6x+5$ finding two numbers that multiply to form $5$ and added form $-6$

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

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Answer

$-\frac{7}{\sqrt[3]{3}}$$\,\,\left(Decimal: -0.5493061443340549\right)$

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