What is the integral of 5x^2-4/x+a ?

The integral of 5x^2-4/x+a is (5x^3)/3-4ln|x|+ax+C

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integral of 5x^2-4/x+a

\int 5 x^{2} - \frac{4}{x} + a d x

\frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x + C

Solution steps

\int 5 x^{2} - \frac{4}{x} + a 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 5 x^{2} d x - \int \frac{4}{x} d x + \int a d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int a d x = a x

= \frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x

Add a constant to the solution

= \frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x + C

What is the integral of 5x^2-4/x+a ?
The integral of 5x^2-4/x+a is (5x^3)/3-4ln|x|+ax+C