What is the integral of (7+3x^{3/2})/(sqrt(x)) ?

The integral of (7+3x^{3/2})/(sqrt(x)) is 14sqrt(x)+(3x^2)/2+C

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integral of (7+3x^{3/2})/(sqrt(x))

\int \frac{7 + 3 x ^{\frac{3}{2}}}{x} d x

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

Solution steps

\int \frac{7 + 3 x ^{\frac{3}{2}}}{x} d x

Expand

\frac{7 + 3 x ^{\frac{3}{2}}}{x} : \frac{7}{x} + 3 x

= \int \frac{7}{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{7}{x} d x + \int 3 x d x

\int \frac{7}{x} d x = 14 x

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

= 14 x + \frac{3 x ^{2}}{2}

Add a constant to the solution

= 14 x + \frac{3 x ^{2}}{2} + C

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What is the integral of (7+3x^{3/2})/(sqrt(x)) ?
The integral of (7+3x^{3/2})/(sqrt(x)) is 14sqrt(x)+(3x^2)/2+C