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

The integral of 2xsqrt(2x) is 2(1/(sqrt(2))x^2sqrt(x)-1/(5sqrt(2))x^{5/2})+C

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integral of 2xsqrt(2x)

\int 2 x 2 x d x

2 (\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}) + C

Solution steps

\int 2 x 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 x 2 x d x

Apply Integration By Parts

: \frac{1}{2} x^{2} x - \int \frac{1}{2 2} x^{\frac{3}{2}} d x

= 2 (\frac{1}{2} x^{2} x - \int \frac{1}{2 2} x^{\frac{3}{2}} d x)

\int \frac{1}{2 2} x^{\frac{3}{2}} d x = \frac{1}{5 2} x^{\frac{5}{2}}

= 2 (\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}})

Add a constant to the solution

= 2 (\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}) + C

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What is the integral of 2xsqrt(2x) ?
The integral of 2xsqrt(2x) is 2(1/(sqrt(2))x^2sqrt(x)-1/(5sqrt(2))x^{5/2})+C