What is the integral of (-11x)/((x^2+5)^2) ?

The integral of (-11x)/((x^2+5)^2) is (11)/(2(x^2+5))+C

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integral of (-11x)/((x^2+5)^2)

\int \frac{- 11 x}{( x ^{2} + 5 ) ^{2}} d x

\frac{11}{2 ( x ^{2} + 5 )} + C

Solution steps

\int \frac{- 11 x}{( x ^{2} + 5 ) ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 11 \cdot \int \frac{x}{( x ^{2} + 5 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{2 u ^{2}} d u

= - 11 \cdot \int \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

= - 11 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 11 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = x^{2} + 5

= - 11 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 5})

Simplify

- 11 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 5}) : \frac{11}{2 ( x ^{2} + 5 )}

= \frac{11}{2 ( x ^{2} + 5 )}

Add a constant to the solution

= \frac{11}{2 ( x ^{2} + 5 )} + C

\int \frac{1}{s ^{2} + 3 s + 6} d s

\frac{d}{d x} (tan^{- 1} (x))

2 x, x^{2}, 0, 2

\int \frac{1}{2} e^{- 2 x} d x

(1, - 8), (5, 4)

What is the integral of (-11x)/((x^2+5)^2) ?
The integral of (-11x)/((x^2+5)^2) is (11)/(2(x^2+5))+C