What is the integral of sqrt(2x) ?

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

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integral of sqrt(2x)

\int 2 x d x

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

Solution steps

\int 2 x d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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