# Evaluate the definite integral. Hint: Use partial fractions. integral 2^3 fraction 5x + 1 2x^2 -...

## Question:

Evaluate the definite integral.

Hint: Use partial fractions.

{eq}\displaystyle \int_2^3 \dfrac{5x + 1}{2x^2 - x - 1} \ dx {/eq}

## Evaluating a Definite Integral:

To solve a definite integral, we must use the Fundamental Theorem of Calculus, i.e.,

{eq}\displaystyle \int_a^b f(x) \ dx = F(x) |_a^b = F(b) - F(a). {/eq}

The result of a definite integral can be zero, a positive number, or a negative number.

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Let's evaluate the definite integral.

{eq}\displaystyle \int_2^3 \dfrac{5x + 1}{2x^2 - x - 1} \ dx {/eq}

Factoring the denominator, we have

{e...