What is the integral of xsqrt(2x) ?

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

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integral of xsqrt(2x)

\int x 2 x d x

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

Solution steps

\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

= \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}}

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

Add a constant to the solution

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

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x \to - 4 lim (x^{2} cos (\frac{5}{x}))

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