What is the Integral of the Square Root of Cosine 2x over the Square of Sine x?

[dickcruz]

Integrte indefinately

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

 

[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

 

[dickcruz]

I do, but there should also be a way to integrate by substitution
ive tried a lot but it doesn't seem to be happening

 

[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

 

[dickcruz]

You get stuck after a while

 

[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.

 

[dickcruz]

We haven't covered that kinda integration .
I need a substitution type result

 

[cristo]

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?

 

[dickcruz]

yeah, it's the right question

 

[dickcruz]

This can't be the solution I'm only in the twelfth grade

 

[dextercioby]

This can't be the solution I'm only in the twelfth grade

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

Daniel.

 

[Gib Z]

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