What is the integral of x/((8-x^2)^2) ?

The integral of x/((8-x^2)^2) is 1/(2(8-x^2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/((8-x^2)^2)

\int \frac{x}{( 8 - x ^{2} ) ^{2}} d x

\frac{1}{2 ( 8 - x ^{2} )} + C

Solution steps

\int \frac{x}{( 8 - x ^{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 = 8 - x^{2}

= - \frac{1}{2} (- \frac{1}{8 - x ^{2}})

Simplify

- \frac{1}{2} (- \frac{1}{8 - x ^{2}}) : \frac{1}{2 ( 8 - x ^{2} )}

= \frac{1}{2 ( 8 - x ^{2} )}

Add a constant to the solution

= \frac{1}{2 ( 8 - x ^{2} )} + C

5 \frac{d y}{d t} + y = 5 t

\int 30 x^{3} 1 + x^{2} d x

\int \frac{- 4 x ^{2}}{4 x - x ^{2}} d x

x \to 0 lim (\frac{x}{1 + x ^{2}})

f (x) = arcsec (2 x)

What is the integral of x/((8-x^2)^2) ?
The integral of x/((8-x^2)^2) is 1/(2(8-x^2))+C