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

The integral from 2 to 4 of x/((x^2+5)^3) is 10/3969

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

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

\frac{10}{3969}

Solution steps

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

Apply u-substitution

: \int_{9}^{21} \frac{1}{2 u ^{3}} d u

= \int_{9}^{21} \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_{9}^{21} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{9}^{21}

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{9}^{21}

Compute the boundaries:

\frac{20}{3969}

= \frac{1}{2} \cdot \frac{20}{3969}

Simplify

= \frac{10}{3969}

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

\int_{0}^{r} r d r

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

\int_{1}^{2} \frac{1}{x x - 1} d x

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

What is the integral from 2 to 4 of x/((x^2+5)^3) ?
The integral from 2 to 4 of x/((x^2+5)^3) is 10/3969