??? 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