What is the integral of (1/(sqrt(x))+(xsqrt(x))/3) ?

The integral of (1/(sqrt(x))+(xsqrt(x))/3) is 2sqrt(x)+2/15 x^{5/2}+C

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integral of (1/(sqrt(x))+(xsqrt(x))/3)

\int (\frac{1}{x} + \frac{x x}{3}) d x

2 x + \frac{2}{15} x^{\frac{5}{2}} + C

Solution steps

\int \frac{1}{x} + \frac{x x}{3} 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{1}{x} d x + \int \frac{x x}{3} d x

\int \frac{1}{x} d x = 2 x

\int \frac{x x}{3} d x = \frac{2}{15} x^{\frac{5}{2}}

= 2 x + \frac{2}{15} x^{\frac{5}{2}}

Add a constant to the solution

= 2 x + \frac{2}{15} x^{\frac{5}{2}} + C

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What is the integral of (1/(sqrt(x))+(xsqrt(x))/3) ?
The integral of (1/(sqrt(x))+(xsqrt(x))/3) is 2sqrt(x)+2/15 x^{5/2}+C