What is the integral of (x^3-5x^2+7)/(x-5) ?

The integral of (x^3-5x^2+7)/(x-5) is (x^3)/3+7ln|x-5|+C

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integral of (x^3-5x^2+7)/(x-5)

\int \frac{x ^{3} - 5 x ^{2} + 7}{x - 5} d x

\frac{x ^{3}}{3} + 7 ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{x ^{3} - 5 x ^{2} + 7}{x - 5} d x

Long division

\frac{x ^{3} - 5 x ^{2} + 7}{x - 5} : x^{2} + \frac{7}{x - 5}

= \int x^{2} + \frac{7}{x - 5} 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{7}{x - 5} d x

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

\int \frac{7}{x - 5} d x = 7 ln ∣ x - 5 ∣

= \frac{x ^{3}}{3} + 7 ln ∣ x - 5 ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + 7 ln ∣ x - 5 ∣ + C

f (x) = θ cos (θ)

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

\int (- 6 x) d x

f (x) = x^{2} + 4, g (x) = - x^{2} - 1, x = - 2, x = 3

f (x) = \frac{x ^{2} - 1}{2 x - 3}

What is the integral of (x^3-5x^2+7)/(x-5) ?
The integral of (x^3-5x^2+7)/(x-5) is (x^3)/3+7ln|x-5|+C