What is the integral from 2 to 3 of x/(sqrt(2x^2-5)) ?

The integral from 2 to 3 of x/(sqrt(2x^2-5)) is (sqrt(13)-sqrt(3))/2

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integral from 2 to 3 of x/(sqrt(2x^2-5))

\int_{2}^{3} \frac{x}{2 x ^{2} - 5} d x

\frac{13 - 3}{2}

Decimal

0.93675 \dots

Solution steps

\int_{2}^{3} \frac{x}{2 x ^{2} - 5} d x

Apply u-substitution

: \int_{3}^{13} \frac{1}{4 u} d u

= \int_{3}^{13} \frac{1}{4 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{3}^{13} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{3}^{13}

= \frac{1}{4} [2 u^{\frac{1}{2}}]_{3}^{13}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{4} [2 u]_{3}^{13}

Compute the boundaries:

213 - 23

= \frac{1}{4} (213 - 23)

Simplify

= \frac{13 - 3}{2}

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What is the integral from 2 to 3 of x/(sqrt(2x^2-5)) ?
The integral from 2 to 3 of x/(sqrt(2x^2-5)) is (sqrt(13)-sqrt(3))/2