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

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

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

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

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

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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y^{^{''}} - 2 y^{^{'}} - 2 y = 0

x \to n - lim ([x])

\frac{d}{d x} ((3 - e^{x})^{8})

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