Artifact 3a77d042f110f512b1f2f7b81caf2d13cc96995d60c56e05f8fce2989a5596ac:
- Executable file
r38/log/trigint.rlg
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 3484) [annotate] [blame] [check-ins using] [more...]
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