Core 3 Substitution by parts Q

See attached.

I'm a bit confused.

I get INTEGRAL (SQRT(U-5) (U^1\2) du/2


But what next?

The mark scheme doesnt help.. Apparently, the x at the start of the question, dissapears somehow but when i did the q, I put that the x becomes (SQRT(U-5)

Thanks in advance

$u=x^2+5$

$\frac{du}{dx}=2x$

$dx=\frac{du}{2x}$

$\int x \times u^{\frac{1}{2}} \frac{du}{2x}$

Can you see that the x will cancel out now?

So becomes

$\frac{1}{2} \int u^{\frac{1}{2}} du$

$=\frac{1}{2} \times \frac{2}{3}u^{\frac{3}{2}}+C$

$=\frac{1}{3}(x^2+5)^{\frac{3}{2}}+C$

You need to work out du/dx