I want to evaluate the improper integral
f(x):=1/(a+sin(x))
integrate(f(x),x,0,2*%pi)
where a>1
The first question Maxima asks is
Is (a-1)*(a+1) positive, negative, or zero?
I reply p
Is sqrt(a^2-1)+a positive or negative?
I give p (that was a trivial question anyway)
Is abs(sqrt(a^2-1)-a)-1 positive, negative, or zero?
I reply n (I had to do a slight calculation)
Is sqrt(a^2-1)+a-1 positive, negative, or zero?
I reply p (another trivial question)
(2*%pi)/sqrt(a^2-1)
The answer is correct, but I wonder what kind of procedure was followed
and I had to specify all those values.
I tried to replace a with b+1 with b positive, but I received 4
questions again with only the first actually needed.
The issue with questions of that type is something that is planned to be
fixed? Where can I read details about this, so I don't post trivial
questions myself?
Another problem I had:
f2(x):=x/(1-cos(x)+x^2);
integrate(f2(x),x,0,2*%pi);
not result was presented (should be 8*%pi/3 if calculation I did by hand
was right).
Seems like Maxima can't handle this integral.