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

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

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

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

\frac{x ^{3}}{3} + 3 ln ∣ x - 3 ∣ + C

Solution steps

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

Long division

\frac{x ^{3} - 3 x ^{2} + 3}{x - 3} : x^{2} + \frac{3}{x - 3}

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

Apply the Sum Rule:

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

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

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

\int \frac{3}{x - 3} d x = 3 ln ∣ x - 3 ∣

= \frac{x ^{3}}{3} + 3 ln ∣ x - 3 ∣

Add a constant to the solution

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

x \to 0 lim (\frac{( - 6 + x ) ^{2} - 36}{x})

\frac{d}{d x} (- x^{3} + 2 x^{2} + 11 x + a)

f (x) = tan (x) sin (6 x^{3})

\frac{d}{d x} (1 0^{x} - 1 0^{- x})

f (x) = (x^{2} - \frac{2}{x})^{- 5}

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