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

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

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

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

\frac{x ^{2}}{2} - 3 x - 5 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

\int 3 d x = 3 x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{2}}{2} - 3 x - 5 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - 3 x - 5 ln ∣ x ∣ + C

\frac{d}{d x} (x^{2} + \frac{432}{x})

\int \frac{1}{3 + x} d x

f (x) = ln (6 x^{3} + e^{x})

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

y^{^{'}} = \frac{y - x}{x}

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