What is the integral of (x^3+8)/x ?

The integral of (x^3+8)/x is (x^3)/3+8ln|x|+C

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integral of (x^3+8)/x

\int \frac{x ^{3} + 8}{x} d x

\frac{x ^{3}}{3} + 8 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{3} + 8}{x} d x

Expand

\frac{x ^{3} + 8}{x} : x^{2} + \frac{8}{x}

= \int x^{2} + \frac{8}{x} 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{8}{x} d x

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

\int \frac{8}{x} d x = 8 ln ∣ x ∣

= \frac{x ^{3}}{3} + 8 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + 8 ln ∣ x ∣ + C

What is the integral of (x^3+8)/x ?
The integral of (x^3+8)/x is (x^3)/3+8ln|x|+C