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

The integral of (4x^2-2/x) is (4x^3)/3-2ln|x|+C

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

\int (4 x^{2} - \frac{2}{x}) d x

\frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + C

f (x) = - x^{2} + 1

\int 1 + 4 x^{2} d x

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

\int \frac{3 ln ( x )}{x ^{2}} d x

\int \frac{y ^{2}}{y} d y

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