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

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

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

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

\frac{x}{2 - x} + ln ∣ 2 - x ∣ + C

Solution steps

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

Apply Integration By Parts

: \frac{x}{2 - x} - \int \frac{1}{2 - x} d x

= \frac{x}{2 - x} - \int \frac{1}{2 - x} d x

\int \frac{1}{2 - x} d x = - ln ∣ 2 - x ∣

= \frac{x}{2 - x} - (- ln ∣ 2 - x ∣)

Simplify

= \frac{x}{2 - x} + ln ∣ 2 - x ∣

Add a constant to the solution

= \frac{x}{2 - x} + ln ∣ 2 - x ∣ + C

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