$\displaystyle \int (1/ \sqrt{x})\ sin\sqrt{x}\ dx\
u=\sqrt{x}\$
the answer is $\displaystyle -2cos(\sqrt{x})+C$ but cant seem to get there
Since they let $\displaystyle u=\sqrt{x}$, this implies that $\displaystyle \,du=\frac{\,dx}{2\sqrt{x}}$
Now, we see that $\displaystyle \int\frac{1}{\sqrt{x}}\sin\sqrt{x}\,dx\implies 2\int\frac{1}{2\sqrt{x}}\sin\sqrt{x}\,dx\implies 2\int\sin u\,du$
Can you take it from here?
--Chris