What is the integral of (12x^2-4x)/(x^2) ?

The integral of (12x^2-4x)/(x^2) is 12x-4ln|x|+C

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integral of (12x^2-4x)/(x^2)

\int \frac{12 x ^{2} - 4 x}{x ^{2}} d x

12 x - 4 ln ∣ x ∣ + C

Solution steps

\int \frac{12 x ^{2} - 4 x}{x ^{2}} d x

Expand

\frac{12 x ^{2} - 4 x}{x ^{2}} : 12 - \frac{4}{x}

= \int 12 - \frac{4}{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 12 d x - \int \frac{4}{x} d x

\int 12 d x = 12 x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 12 x - 4 ln ∣ x ∣

Add a constant to the solution

= 12 x - 4 ln ∣ x ∣ + C

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What is the integral of (12x^2-4x)/(x^2) ?
The integral of (12x^2-4x)/(x^2) is 12x-4ln|x|+C