Mon Jan 4 00:09:22 MET 1999
REDUCE 3.7, 15-Jan-99 ...
1: 1:
2: 2: 2: 2: 2: 2: 2: 2: 2:
3: 3: % 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
***** system can't integrate after
subs
end;
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Time for test: 4220 ms, plus GC time: 140 ms
5: 5:
Quitting
Mon Jan 4 00:09:35 MET 1999