Indefinate integration

1. Jan 15, 2007

dickcruz

Integrte indefinately

(Cos2x)^1/2
------------- . dx
Sin^2 x

2. Jan 15, 2007

sara_87

did you not attempt this question?
the people on this board will be more willing to help after they have seen what you've done.

also your question is unclear did you mean: [(cos(2x))^(1/2)]/[(sinx)^2] ?

if so do you know how to integrate by parts

3. Jan 15, 2007

dickcruz

I do, but there should also be a way to integrate by substitution
ive tried a lot but it doesnt seem to be happening

4. Jan 15, 2007

Gib Z

Try using trig identites. Cos 2x=cos^2 x - sin^2 x = 2cos^2 x -1

Sin^2 x= 1-Cos^2 x

5. Jan 15, 2007

dickcruz

You get stuck after a while

6. Jan 16, 2007

dextercioby

$$\int \frac{\sqrt{\cos 2x}}{\sin^{2}x} dx =-\sqrt{\cos 2x}\cot x-E(x,2)-F(x,2) +C$$

, where E and F are the elliptic integrals of the second and first kind, respectively.

Daniel.

7. Jan 16, 2007

dickcruz

We havent covered that kinda integration .
I need a substitution type result

8. Jan 16, 2007

cristo

Staff Emeritus
dextercioby has given you the solution. In general, elliptic integrals cannot be expressed in terms of elementary functions. Are you sure you've written down the question correctly?

9. Jan 16, 2007

dickcruz

yeah, it's the right question

10. Jan 16, 2007

dickcruz

This cant be the solution I'm only in the twelfth grade

11. Jan 17, 2007

dextercioby

Well, that IS the solution and there's no way you can circumvent it and find another one with only "elementary" functions.

Daniel.

12. Jan 17, 2007

Gib Z

Bad luck kiddo. If your teacher tells you how to get another result, we want to hear :)