Artifact 02f15f5cdbbc1d3483c482112cd891dc10b0d2992ccc7aef5226b1e2bc6cc0a4:

• Executable file r38/packages/trigint/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 Feb 10 12:28:49 2004 run on Linux
% 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: 550 ms, plus GC time: 20 ms