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

The integral of (x^2)/((1-x)^2) is (x^3)/((1-x)^2)-(x^2)/((1-x)^2)+2ln|1-x|+2/(1-x)+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)/((1-x)^2)

\int \frac{x ^{2}}{( 1 - x ) ^{2}} d x

\frac{x ^{3}}{( 1 - x ) ^{2}} - \frac{x ^{2}}{( 1 - x ) ^{2}} + 2 ln ∣ 1 - x ∣ + \frac{2}{1 - x} + C

Solution steps

\int \frac{x ^{2}}{( 1 - x ) ^{2}} d x

Apply Integration By Parts

: \frac{x ^{3}}{( 1 - x ) ^{2}} - \int \frac{2 x ^{2}}{( 1 - x ) ^{3}} d x

= \frac{x ^{3}}{( 1 - x ) ^{2}} - \int \frac{2 x ^{2}}{( 1 - x ) ^{3}} d x

\int \frac{2 x ^{2}}{( 1 - x ) ^{3}} d x = \frac{x ^{2}}{( 1 - x ) ^{2}} - 2 ln ∣ 1 - x ∣ - \frac{2}{1 - x}

= \frac{x ^{3}}{( 1 - x ) ^{2}} - (\frac{x ^{2}}{( 1 - x ) ^{2}} - 2 ln ∣ 1 - x ∣ - \frac{2}{1 - x})

Simplify

= \frac{x ^{3}}{( 1 - x ) ^{2}} - \frac{x ^{2}}{( 1 - x ) ^{2}} + 2 ln ∣ 1 - x ∣ + \frac{2}{1 - x}

Add a constant to the solution

= \frac{x ^{3}}{( 1 - x ) ^{2}} - \frac{x ^{2}}{( 1 - x ) ^{2}} + 2 ln ∣ 1 - x ∣ + \frac{2}{1 - x} + C

\int 0.024 \cdot (0.03 q^{2} - 2 q) + 130 d q

\int \frac{x - 2}{x ^{2} - 6 x} d x

\int x^{2} (a^{2} - x^{2})^{2} d x

\int \frac{1}{( t + 2 ) ^{2} ( t + 1 )} d t

What is the integral of (x^2)/((1-x)^2) ?
The integral of (x^2)/((1-x)^2) is (x^3)/((1-x)^2)-(x^2)/((1-x)^2)+2ln|1-x|+2/(1-x)+C