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

The integral from-2 to-1 of x/((x^2+3)^2) is -3/56

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integral from-2 to-1 of x/((x^2+3)^2)

\int_{- 2}^{- 1} \frac{x}{( x ^{2} + 3 ) ^{2}} d x

- \frac{3}{56}

Decimal

- 0.05357 \dots

Solution steps

\int_{- 2}^{- 1} \frac{x}{( x ^{2} + 3 ) ^{2}} d x

Apply u-substitution

: \int_{7}^{4} \frac{1}{2 u ^{2}} d u

= \int_{7}^{4} \frac{1}{2 u ^{2}} d u

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

= - \int_{4}^{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_{4}^{7} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{4}^{7}

= - \frac{1}{2} [- \frac{1}{u}]_{4}^{7}

Compute the boundaries:

\frac{3}{28}

= - \frac{1}{2} \cdot \frac{3}{28}

Simplify

= - \frac{3}{56}

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\int_{0}^{1} 3 t^{3} d t

What is the integral from-2 to-1 of x/((x^2+3)^2) ?
The integral from-2 to-1 of x/((x^2+3)^2) is -3/56