What is the integral of 3/x-2sqrt(x)+18 ?

The integral of 3/x-2sqrt(x)+18 is 3ln|x|-4/3 x^{3/2}+18x+C

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integral of 3/x-2sqrt(x)+18

\int \frac{3}{x} - 2 x + 18 d x

3 ln ∣ x ∣ - \frac{4}{3} x^{\frac{3}{2}} + 18 x + C

Solution steps

\int \frac{3}{x} - 2 x + 18 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 \frac{3}{x} d x - \int 2 x d x + \int 18 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

\int 18 d x = 18 x

= 3 ln ∣ x ∣ - \frac{4}{3} x^{\frac{3}{2}} + 18 x

Add a constant to the solution

= 3 ln ∣ x ∣ - \frac{4}{3} x^{\frac{3}{2}} + 18 x + C

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What is the integral of 3/x-2sqrt(x)+18 ?
The integral of 3/x-2sqrt(x)+18 is 3ln|x|-4/3 x^{3/2}+18x+C