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

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

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integral of 2sqrt(2x)

\int 2 2 x d x

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

Solution steps

\int 2 2 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int 2 x d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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