What is the integral of (3+4x^{3/2})/(sqrt(x)) ?

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

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integral of (3+4x^{3/2})/(sqrt(x))

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

6 x + 2 x^{2} + C

Solution steps

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

Expand

\frac{3 + 4 x ^{\frac{3}{2}}}{x} : \frac{3}{x} + 4 x

= \int \frac{3}{x} + 4 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 4 x d x

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

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

= 6 x + 2 x^{2}

Add a constant to the solution

= 6 x + 2 x^{2} + C

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