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

The integral of x/((x^2+2)^2) is -1/(2(x^2+2))+C

Popular >

integral of x/((x^2+2)^2)

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

- \frac{1}{2 ( x ^{2} + 2 )} + C

Solution steps

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

Apply u-substitution

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

= \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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = x^{2} + 2

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

Simplify

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

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

Add a constant to the solution

= - \frac{1}{2 ( x ^{2} + 2 )} + C

\frac{d}{d x} (0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300)

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

\int \frac{- 2}{x} d x

\frac{15 + 5 5}{12} a^{3}

(1 + x^{2}) y^{^{''}} = 2 x (y^{^{'}})^{2}

What is the integral of x/((x^2+2)^2) ?
The integral of x/((x^2+2)^2) is -1/(2(x^2+2))+C