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

The integral of (x^2)/(x-2) is ((x-2)^2)/2+4(x-2)+4ln|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^2)/(x-2)

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

\frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{( u + 2 ) ^{2}}{u} d u

= \int \frac{( u + 2 ) ^{2}}{u} d u

Expand

\frac{( u + 2 ) ^{2}}{u} : u + 4 + \frac{4}{u}

= \int u + 4 + \frac{4}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u + \int 4 d u + \int \frac{4}{u} d u

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

\int 4 d u = 4 u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

= \frac{u ^{2}}{2} + 4 u + 4 ln ∣ u ∣

Substitute back

u = x - 2

= \frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣

Add a constant to the solution

= \frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣ + C

\int (e^{x} + 1)^{3} e^{x} d x

\int e^{i 8 x} cos (5 x) d x

x \to 0 + lim (x cot (x) csc (x))

x^{4}, at x = 3

\frac{d}{d x} (\frac{16}{( 1 + 2 x ) ^{3}})

What is the integral of (x^2)/(x-2) ?
The integral of (x^2)/(x-2) is ((x-2)^2)/2+4(x-2)+4ln|x-2|+C