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

The integral from 2 to 3 of x/((x^2-2)^2) is 5/28

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

\int_{2}^{3} \frac{x}{( x ^{2} - 2 ) ^{2}} d x

\frac{5}{28}

Decimal

0.17857 \dots

Solution steps

\int_{2}^{3} \frac{x}{( x ^{2} - 2 ) ^{2}} d x

Apply u-substitution

: \int_{2}^{7} \frac{1}{2 u ^{2}} d u

= \int_{2}^{7} \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2}^{7} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{2}^{7}

= \frac{1}{2} [- \frac{1}{u}]_{2}^{7}

Compute the boundaries:

\frac{5}{14}

= \frac{1}{2} \cdot \frac{5}{14}

Simplify

= \frac{5}{28}

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What is the integral from 2 to 3 of x/((x^2-2)^2) ?
The integral from 2 to 3 of x/((x^2-2)^2) is 5/28