# Thread: help with this integral

1. ## help with this integral

i'm trying to find the length of a curve, and i've gotten it down to where i need to take the integral of the derivatives squared added together blah blah blah. anyways, how do i find the integral of (2+2cos(x))^1/2 ?
could i use u substitution? i didn't think so because then i'd have a sin (x) to deal with, and i don't think that'd work. with the whole thing being in a square root, i can't just integrate them invidually, correct? so i'm stuck. can anyone help?

2. $\displaystyle \int\sqrt{2+2cos(x)}dx$

Let $\displaystyle x=2tan^{-1}(u), \;\ dx=\frac{2}{u^{2}+1}du, \;\ u=tan(\frac{x}{2})$

Making the subs brings us to:

$\displaystyle 4\int (u^{2}+1)^{\frac{-3}{2}}du$

Can you finish now?. An appropriate sub, say w, will get it to

$\displaystyle u=tan(w), \;\ du=sec^{2}(w)dw$

$\displaystyle 4\int\frac{sec^{2}(w)}{sec^{3}(w)}dw=4\int\frac{1} {sec(w)}dw=4\int cos(w)dw$

3. Originally Posted by isuckatcalc
i'm trying to find the length of a curve, and i've gotten it down to where i need to take the integral of the derivatives squared added together blah blah blah ...
mind telling us the equation for the original curve and the limits for which you are to find the arc length?

4. thanks guys, i got it.