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

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

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integral of (sqrt(x)+3x)

\int (x + 3 x) d x

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

Solution steps

\int 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 x d x + \int 3 x d x

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

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

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

Add a constant to the solution

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

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