What is the integral of (x^2)/((x-3)^2) ?

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

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integral of (x^2)/((x-3)^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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