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

= 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

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