\(\displaystyle \int x(\sqrt{2x+1} dx = \frac{1}{15}(2x+1)^{\frac{3}{2}} (3x-1) + c \)

I have done this so many times and keep getting the wrong answer, heres my working.

\(\displaystyle u = \sqrt{2x+1} \)

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

\(\displaystyle \frac{dx}{du} = u \)

\(\displaystyle dx = u du \)

\(\displaystyle \int \frac{1}{2}(u^{2} -1) u u du \)

\(\displaystyle \frac{1}{2} \int (u^{4} -u^{2}) du \)

\(\displaystyle \frac{1}{2}\int (\frac{u^{5}}{5} - \frac{u^{3}}{3}) \)

\(\displaystyle \frac{1}{2} (\frac{3u^{5} -5u^{3}}{15} ) \)

\(\displaystyle \frac{1}{2} \times \frac{1}{15} ( 3u^{5} - 5u^{3}) \)

From here I am unable to get the desired expression, any help suggestions as to where I am going wrong would be greatly appreciated.

thanks