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

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

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integral of (3+xsqrt(x))

\int (3 + x x) d x

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

Solution steps

\int 3 + x 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 x x d x

\int 3 d x = 3 x

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

= 3 x + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 3 x + \frac{2}{5} x^{\frac{5}{2}} + C

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