What is the integral from 2 to 6 of x/((x^2+8)^3) ?

The integral from 2 to 6 of x/((x^2+8)^3) is 7/4356

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integral from 2 to 6 of x/((x^2+8)^3)

\int_{2}^{6} \frac{x}{( x ^{2} + 8 ) ^{3}} d x

\frac{7}{4356}

Decimal

0.00160 \dots

Solution steps

\int_{2}^{6} \frac{x}{( x ^{2} + 8 ) ^{3}} d x

Apply u-substitution

: \int_{12}^{44} \frac{1}{2 u ^{3}} d u

= \int_{12}^{44} \frac{1}{2 u ^{3}} 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_{12}^{44} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{12}^{44}

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{12}^{44}

Compute the boundaries:

\frac{7}{2178}

= \frac{1}{2} \cdot \frac{7}{2178}

Simplify

= \frac{7}{4356}

\int_{- 2}^{0} 2 x^{3} - 8 x d x

\int_{1}^{3} \frac{2 x}{( x ^{2} + 4 ) ^{3}} d x

\int_{- 4}^{0} (5 + 16 - x^{2}) d x

\int_{- 1}^{1} \frac{1}{x} d x

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

What is the integral from 2 to 6 of x/((x^2+8)^3) ?
The integral from 2 to 6 of x/((x^2+8)^3) is 7/4356