intergrating int [ (2/3) cos(Sqrt[x]) ] dx using chart

[kpx001]

how would i integrate int [ (2/3) cos(Sqrt[x]) ] dx using the antiderivative chart? i tried using formula #47 but the du has

$\displaystyle \frac{1}{2\sqrt{x}}$

and i cant figure this out.

The entire problem is $\displaystyle \int\frac{cos^{3}(\sqrt{x})}{\sqrt{x}}dx$.

 

[galactus]

Re: intergrating (2/3)cos[Sqrt[x]]

Is this it, including the 2/3?.

$\displaystyle \frac{2}{3}\int\frac{cos^{3}(\sqrt{x})}{\sqrt{x}}dx$

If so, let $\displaystyle u=\sqrt{x}, \;\ du=\frac{1}{2\sqrt{x}}dx, \;\ 2du=\frac{1}{\sqrt{x}}dx$

Make the subs:

$\displaystyle \frac{4}{3}\int{cos^{3}(u)}du$

You had the correct substitution, you just needed to multiply by 2 to get 2du

 

[stapel]

i tried using formula #47 but...

Kindly keep in mind that we aren't in your classroom and don't have your textbook; you'll need to provide whatever formulae, variables, or algorithms you're using.

Thank you!

Eliz.