Step-by-step Solution

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

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$-0.5493061443340549$

Step-by-step explanation

Problem to solve:

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

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

$\begin{matrix}\left(-1\right)\left(-5\right)=5\\ \left(-1\right)+\left(-5\right)=-6\end{matrix}$
2

Thus

$\int_{2}^{4}\frac{1}{\left(x-1\right)\left(x-5\right)}dx$

$-0.5493061443340549$
$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Main topic:

Integrals by partial fraction expansion

~ 1.33 seconds

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