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

The integral of (3sqrt(x)+(2))/((sqrt(x))) is 3x+4sqrt(x)+C

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

\int \frac{3 x + ( 2 )}{( x )} d x

3 x + 4 x + C

Solution steps

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

Expand

\frac{3 x + 2}{x} : 3 + \frac{2}{x}

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

\int 3 d x = 3 x

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

= 3 x + 4 x

Add a constant to the solution

= 3 x + 4 x + C

What is the integral of (3sqrt(x)+(2))/((sqrt(x))) ?
The integral of (3sqrt(x)+(2))/((sqrt(x))) is 3x+4sqrt(x)+C