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

Integrate 1/(-6x+5+x^2) from 2 to 4

Answer

$-\frac{7}{\sqrt[3]{3}}$

Step-by-step explanation

Problem

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

Factor the trinomial $5-6x+x^2$ finding two numbers that multiply to form $5$ and added form $-6$

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

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Answer

$-\frac{7}{\sqrt[3]{3}}$