What is the integral from-3 to-2 of x/((x^2+6)^2) ?

The integral from-3 to-2 of x/((x^2+6)^2) is -1/60

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integral from-3 to-2 of x/((x^2+6)^2)

\int_{- 3}^{- 2} \frac{x}{( x ^{2} + 6 ) ^{2}} d x

- \frac{1}{60}

Decimal

- 0.01666 \dots

Solution steps

\int_{- 3}^{- 2} \frac{x}{( x ^{2} + 6 ) ^{2}} d x

Apply u-substitution

: \int_{15}^{10} \frac{1}{2 u ^{2}} d u

= \int_{15}^{10} \frac{1}{2 u ^{2}} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{10}^{15} \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_{10}^{15} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{10}^{15}

= - \frac{1}{2} [- \frac{1}{u}]_{10}^{15}

Compute the boundaries:

\frac{1}{30}

= - \frac{1}{2} \cdot \frac{1}{30}

Simplify

= - \frac{1}{60}

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What is the integral from-3 to-2 of x/((x^2+6)^2) ?
The integral from-3 to-2 of x/((x^2+6)^2) is -1/60