What is the integral of (x^3-3x^2+5)/((x-3)) ?

The integral of (x^3-3x^2+5)/((x-3)) is (x^3)/3+5ln|x-3|+C

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integral of (x^3-3x^2+5)/((x-3))

\int \frac{x ^{3} - 3 x ^{2} + 5}{( x - 3 )} d x

\frac{x ^{3}}{3} + 5 ln ∣ x - 3 ∣ + C

Solution steps

\int \frac{x ^{3} - 3 x ^{2} + 5}{x - 3} d x

Long division

\frac{x ^{3} - 3 x ^{2} + 5}{x - 3} : x^{2} + \frac{5}{x - 3}

= \int x^{2} + \frac{5}{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{5}{x - 3} d x

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

\int \frac{5}{x - 3} d x = 5 ln ∣ x - 3 ∣

= \frac{x ^{3}}{3} + 5 ln ∣ x - 3 ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + 5 ln ∣ x - 3 ∣ + C

x \to 1 lim (\frac{1}{x ^{2} - 1})

\frac{s}{( s - 1 ) ^{2} + 1}

\int_{1}^{5} 2 e^{2 x} d x

x \to - 0.001 lim (4 x^{2} + 7)

What is the integral of (x^3-3x^2+5)/((x-3)) ?
The integral of (x^3-3x^2+5)/((x-3)) is (x^3)/3+5ln|x-3|+C