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

The integral of sqrt(2x)+sqrt(x/2) is sqrt(2)xsqrt(x)+C

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integral of sqrt(2x)+sqrt(x/2)

\int 2 x + \frac{x}{2} d x

2 x x + C

Solution steps

\int 2 x + \frac{x}{2} 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 2 x d x + \int \frac{x}{2} d x

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

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

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

Add similar elements:

- \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{3} x^{\frac{3}{2}} = 0

= 2 x x

Add a constant to the solution

= 2 x x + C

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What is the integral of sqrt(2x)+sqrt(x/2) ?
The integral of sqrt(2x)+sqrt(x/2) is sqrt(2)xsqrt(x)+C