Why can't maxima evaluate this integral



??? a ?crit :
> I used Maxima to calculate a integral,that is \int_0^\theta 
> {\frac{1}{{\sqrt {1 - \frac{{{{\cos }^2}\theta }}{{{{\cos }^2}x}}} 
> }}{\rm{d}}x}(1/sqrt(1-cos(a)^2/cos(x)^2)),but Maxima gives nothing.
> But when I changed its form into \int_0^\theta {\frac{{{{\cos 
> }^2}x}}{{\sqrt {{{\cos }^2}x - {{\cos }^2}\theta } 
> }}{\rm{d}}x}(cos(x)/sqrt(cos(x)^2-cos(a)^2)),it successfully evaluates.
> What is wrong with Maxima?Why can't it evaluate the first form of 
> integral?
Maybe because the integrands are not the same :  cos^2(x) should be only 
cos(x) in the first numerator of second form.

With Maxima 5.20.1 I don't get any answer, wether I put cos(x) or 
cos^2(x) in the numerator :

(%i2) 
integrate(1/sqrt(1-cos(t)^2/cos(x)^2)/sqrt(1-cos(a)^2/cos(x)^2),x,0,t);
Is  cos(x)  positive or negative?
p;
Is  t  positive, negative, or zero?
p;
(%o2) 
'integrate(1/(sqrt(1-cos(a)^2/cos(x)^2)*sqrt(1-cos(t)^2/cos(x)^2)),x,0,t)
(%i3) 
integrate(cos(x)/sqrt(cos(x)^2-cos(t)^2)*cos(x)/sqrt(cos(x)^2-cos(a)^2),x,0,t);
Is  t  positive, negative, or zero?
p;
(%o3) 
'integrate(cos(x)^2/(sqrt(cos(x)^2-cos(a)^2)*sqrt(cos(x)^2-cos(t)^2)),x,0,t)
(%i4) 
integrate(cos(x)^2/sqrt(cos(x)^2-cos(t)^2)*cos(x)/sqrt(cos(x)^2-cos(a)^2),x,0,t);
Is  t  positive, negative, or zero?
p;
(%o4) 
'integrate(cos(x)^3/(sqrt(cos(x)^2-cos(a)^2)*sqrt(cos(x)^2-cos(t)^2)),x,0,t)

Eric