Integrating dx/( a+b sin(x))



On 9/18/2012 11:55 PM, Guille Rmo wrote:
> I was trying to do
>
>      integrate( 1 / ( a+b*sin(x) ), x)
>
> and I got this:
> (2.0*atan((0.5*((2*a*sin(x))/(cos(x)+1)+2*b))/(a^2-b^2)^0.5))/(a^2-b^2)^0.5
Why don't you say what you did?  You seem to have done something to 
insert floating point numbers
into this answer. This is generally a bad idea unless you expect to 
resolve everything together into a
single floating-point number, and that is impossible with symbols like a 
and b in the expression.
(a^2-b^2)^(0.5)   is NOT treated the same as sqrt(a^2-b^2).

> But if I evaluate this from 0 to 2pi (I was trying to get the Laplace 
> transform of the zeroth Bessel function) I get some weird stuff.
Why don't you use definite integration,   integrate(f,x,0,2*%pi)  ?

As for whether you have encountered a bug or not -- I suggest you say 
EXACTLY the sequence of commands you used so
that other people could try them.