What is the integral of (x^2+17)/x ?

The integral of (x^2+17)/x is (x^2)/2+17ln|x|+C

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integral of (x^2+17)/x

\int \frac{x ^{2} + 17}{x} d x

\frac{x ^{2}}{2} + 17 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{2} + 17}{x} d x

Expand

\frac{x ^{2} + 17}{x} : x + \frac{17}{x}

= \int x + \frac{17}{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 d x + \int \frac{17}{x} d x

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

\int \frac{17}{x} d x = 17 ln ∣ x ∣

= \frac{x ^{2}}{2} + 17 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 17 ln ∣ x ∣ + C

\frac{\partial}{\partial x} ((5 x + 2 y) (e^{y}))

2 x^{2} + 2 x

\int e^{6 x} sin (3 x) d x

\frac{\partial}{\partial x} (x ln (\frac{x}{y ^{2}}))

n \to \infty lim (ln (2))

What is the integral of (x^2+17)/x ?
The integral of (x^2+17)/x is (x^2)/2+17ln|x|+C