What is the integral of (6x^2-5)/x ?

The integral of (6x^2-5)/x is 3x^2-5ln|x|+C

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integral of (6x^2-5)/x

\int \frac{6 x ^{2} - 5}{x} d x

3 x^{2} - 5 ln ∣ x ∣ + C

Solution steps

\int \frac{6 x ^{2} - 5}{x} d x

Expand

\frac{6 x ^{2} - 5}{x} : 6 x - \frac{5}{x}

= \int 6 x - \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 6 x d x - \int \frac{5}{x} d x

\int 6 x d x = 3 x^{2}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 3 x^{2} - 5 ln ∣ x ∣

Add a constant to the solution

= 3 x^{2} - 5 ln ∣ x ∣ + C

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x \to 0 lim ((1 + x)^{x})

What is the integral of (6x^2-5)/x ?
The integral of (6x^2-5)/x is 3x^2-5ln|x|+C