What is the integral of 8x^3-12x^2+4/x ?

The integral of 8x^3-12x^2+4/x is 2x^4-4x^3+4ln|x|+C

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integral of 8x^3-12x^2+4/x

\int 8 x^{3} - 12 x^{2} + \frac{4}{x} d x

2 x^{4} - 4 x^{3} + 4 ln ∣ x ∣ + C

Solution steps

\int 8 x^{3} - 12 x^{2} + \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 8 x^{3} d x - \int 12 x^{2} d x + \int \frac{4}{x} d x

\int 8 x^{3} d x = 2 x^{4}

\int 12 x^{2} d x = 4 x^{3}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 2 x^{4} - 4 x^{3} + 4 ln ∣ x ∣

Add a constant to the solution

= 2 x^{4} - 4 x^{3} + 4 ln ∣ x ∣ + C

What is the integral of 8x^3-12x^2+4/x ?
The integral of 8x^3-12x^2+4/x is 2x^4-4x^3+4ln|x|+C