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

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

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integral of 3/(sqrt(x))+3sqrt(x)

\int \frac{3}{x} + 3 x d x

6 x + 2 x^{\frac{3}{2}} + C

Solution steps

\int \frac{3}{x} + 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 \frac{3}{x} d x + \int 3 x d x

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

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

= 6 x + 2 x^{\frac{3}{2}}

Add a constant to the solution

= 6 x + 2 x^{\frac{3}{2}} + C

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