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

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

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integral of (3-sqrt(x)+x)

\int (3 - x + x) d x

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

\int 3 d x = 3 x

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

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

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

Add a constant to the solution

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

\int \frac{sec ^{2} ( 2 x )}{1 + 3 tan ^{2} ( 2 x )} d x

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\int x e^{(x^{2} - 1)} d x

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