What is the integral from-4 to-3 of x/((x^2+5)^2) ?

The integral from-4 to-3 of x/((x^2+5)^2) is -1/84

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integral from-4 to-3 of x/((x^2+5)^2)

\int_{- 4}^{- 3} \frac{x}{( x ^{2} + 5 ) ^{2}} d x

- \frac{1}{84}

Decimal Notation

- 0.01190 \dots

Solution steps

\int_{- 4}^{- 3} \frac{x}{( x ^{2} + 5 ) ^{2}} d x

Apply u-substitution

: \int_{21}^{14} \frac{1}{2 u ^{2}} d u

= \int_{21}^{14} \frac{1}{2 u ^{2}} d u

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

= - \int_{14}^{21} \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_{14}^{21} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{14}^{21}

= - \frac{1}{2} [- \frac{1}{u}]_{14}^{21}

Compute the boundaries:

\frac{1}{42}

= - \frac{1}{2} \cdot \frac{1}{42}

Simplify

= - \frac{1}{84}

\int_{0}^{4} (x^{2} - 1) d x

\int_{0}^{2} 12 x^{3} d x

\int_{1}^{6} 8 x^{3} - 6 x^{- 2} d x

\int_{0}^{1} (1 + x^{2}) d x

\int_{0}^{1} 2 x^{2} - 2 x^{3} d x

What is the integral from-4 to-3 of x/((x^2+5)^2) ?
The integral from-4 to-3 of x/((x^2+5)^2) is -1/84