What is the integral of (sqrt(3)+sqrt(x))^2 ?

The integral of (sqrt(3)+sqrt(x))^2 is 3x+4/(sqrt(3))x^{3/2}+(x^2)/2+C

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integral of (sqrt(3)+sqrt(x))^2

\int (3 + x)^{2} d x

3 x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Solution steps

\int (3 + x)^{2} d x

Expand

(3 + x)^{2} : 3 + 23 x + x

= \int 3 + 23 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 23 x d x + \int x d x

\int 3 d x = 3 x

\int 23 x d x = \frac{4}{3} x^{\frac{3}{2}}

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

= 3 x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Add a constant to the solution

= 3 x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

f (x) = - x^{2}

x \to 7 lim (\frac{3}{x - 7})

x \to 0 lim (\frac{3 x}{x ^{2} + 2 x})

\frac{2}{x}

\frac{\partial}{\partial x} (4 - x)

What is the integral of (sqrt(3)+sqrt(x))^2 ?
The integral of (sqrt(3)+sqrt(x))^2 is 3x+4/(sqrt(3))x^{3/2}+(x^2)/2+C