Integrate (1-k^2 cos(x)^2)^(-3/2)

[nazmulislam]

I want to integrate (1-k^2 cos(x)^2)^(-3/2) with lower limit 0 and upper limit pi/2, where x is the variable and k is the constant.

 

[SammyS]

I want to integrate (1-k^2 cos(x)^2)^(-3/2) with lower limit 0 and upper limit pi/2, where x is the variable and k is the constant.

Hello nazmulislam. Welcome to PF !

According to the rules of this Forum, you have to show an attempt at the solution, before we can help you.

 

[nazmulislam]

I tried to integrate by parts. Suppose u=1/(1-k^2 cos(x)^2) and v=1/(1-k^2 cos(x)^2)^(1/2). Then, I made dv/dx and tried to integrate u*(dv/dx) by parts. I did in this way because the results involve complete elliptic integrals of second kind. But I couldn't finish, because I got very complex expressions.