This one doesn't seem like an integration by parts problem.
Integration by parts $\displaystyle \int udv = uv - \int vdu$
$\displaystyle \int 3\cos \sqrt{x} dx$
$\displaystyle \int 3\cos x^{1/2} dx$
What is the next step? What is u? What is dv?
This one doesn't seem like an integration by parts problem.
Integration by parts $\displaystyle \int udv = uv - \int vdu$
$\displaystyle \int 3\cos \sqrt{x} dx$
$\displaystyle \int 3\cos x^{1/2} dx$
What is the next step? What is u? What is dv?
Write it out like this:
$\displaystyle \begin{align*} \int{ 3\cos{ \left( \sqrt{x} \right) } \, \mathrm{d}x} &= 6 \int{ \sqrt{x} \cos{ \left( \sqrt{x} \right) } \, \frac{1}{2\sqrt{x}}\,\mathrm{d}x } \end{align*}$
Then make the substitution $\displaystyle \begin{align*} X = \sqrt{x} \implies \mathrm{d}X = \frac{1}{2\sqrt{x}}\,\mathrm{d}x \end{align*}$ and the integral becomes
$\displaystyle \begin{align*} 6\int{ \sqrt{x}\cos{ \left( \sqrt{x} \right) } \, \frac{1}{2\sqrt{x}} \, \mathrm{d}x } &= 6 \int{ X \cos{(X)}\,\mathrm{d}X } \end{align*}$
and now you can apply integration by parts.