What is the integral of 6sqrt(x)-3/x ?

The integral of 6sqrt(x)-3/x is 4x^{3/2}-3ln|x|+C

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integral of 6sqrt(x)-3/x

\int 6 x - \frac{3}{x} d x

4 x^{\frac{3}{2}} - 3 ln ∣ x ∣ + C

Solution steps

\int 6 x - \frac{3}{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 6 x d x - \int \frac{3}{x} d x

\int 6 x d x = 4 x^{\frac{3}{2}}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 4 x^{\frac{3}{2}} - 3 ln ∣ x ∣

Add a constant to the solution

= 4 x^{\frac{3}{2}} - 3 ln ∣ x ∣ + C

What is the integral of 6sqrt(x)-3/x ?
The integral of 6sqrt(x)-3/x is 4x^{3/2}-3ln|x|+C