Tue Apr 15 00:35:10 2008 run on win32
% some test examples for the trigint package. If the input expression is
% free of sin, cos or tan at the moment, then no Weierstrass substitutions
% will be made, and the standard int operator is called.
trigint(1/x,x);
log(x)
trigint(1,y);
x
trigint(sin(x),x);
pi + 2*x
- 2*tan(----------)
4
----------------------
pi + 2*x 2
tan(----------) + 1
4
trigint(1/(cos(x)+2),x);
x
tan(---)
2 - pi + x
2*sqrt(3)*(atan(----------) + floor(-----------)*pi)
sqrt(3) 2*pi
------------------------------------------------------
3
trigint(1/(cos(x)-2),x);
x
3*tan(---)
2 - pi + x
- 2*sqrt(3)*(atan(------------) + floor(-----------)*pi)
sqrt(3) 2*pi
-----------------------------------------------------------
3
trigint(1/(sin(x)),x);
pi + 2*x pi + 2*x
log(tan(----------) - 1) - log(tan(----------) + 1)
4 4
trigint(1/(sin(x)+2),x);
pi + 2*x
3*tan(----------)
4 - pi + 2*x
2*sqrt(3)*(atan(-------------------) + floor(-------------)*pi)
sqrt(3) 4*pi
-----------------------------------------------------------------
3
trigint(15/(cos(x)*(5-4*cos(x))),x);
x - pi + x x
8*atan(3*tan(---)) + 8*floor(-----------)*pi - 3*log(tan(---) - 1)
2 2*pi 2
x
+ 3*log(tan(---) + 1)
2
trigint(3/(5+4*sin(x)),x);
pi + 2*x - pi + 2*x
2*(atan(3*tan(----------)) + floor(-------------)*pi)
4 4*pi
trigint(3/(5-4*cos(x)),x);
x - pi + x
2*(atan(3*tan(---)) + floor(-----------)*pi)
2 2*pi
trigint(tan(x),x);
x
2*atan(tan(---))*tan(x)
2
%trigint(sqrt(cos(x)),x);
on tracetrig;
trigint(1/(cos(x)-5),x);
x
3*tan(---)
2 - pi + x
- sqrt(6)*(atan(------------) + floor(-----------)*pi)
sqrt(6) 2*pi
---------------------------------------------------------
6
trigint(1/(sqrt(sin(x))),x);
failed with substitution B: system could not
integrate after subs, trying A
failed with A: trying C now
failed with C: trying D now
trying all possible substitutions
- pi + 2*x - pi + 2*x
- floor(-------------)*sign(i)*infinity + floor(-------------)*infinity
2*pi 2*pi
2 1/4
(u + 1)
+ sub(u=tan(x),int(----------------------,u))
2
sqrt(u)*u + sqrt(u)
end;
Time for test: 628 ms, plus GC time: 26 ms