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

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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

y = e^{1 - x}

\frac{d}{d x} (ln^{2} (3 x))

F (s) = (\frac{2}{s} - \frac{1}{s ^{3}})^{2}

\int (1 + 2 x^{2}) e^{x^{2}} d x

x \to 3 lim (x 13 - x^{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