Artifact acf228e7e5b1a315b2cf340529d75df4398a852fbbadb346a8dc92f7e3b11c3b:
- File
r34.1/lib/tritstx.tex
— 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: 7054) [annotate] [blame] [check-ins using] [more...]
- File
r34/lib/tritstx.tex
— 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: 7054) [annotate] [blame] [check-ins using]
\TRIexa{Integration}{TeXindent}{1000}{int(1+x+x**2,x);} $$\displaylines{\qdd \frac{x\cdot \(2\cdot x^{2} +3\cdot x +6 \) }{ 6} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x**2*(2*x**2+x)**2,x);} $$\displaylines{\qdd \frac{x^{5}\cdot \(60\cdot x^{2} +70\cdot x +21 \) }{ 105} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x*(x**2+2*x+1),x);} $$\displaylines{\qdd \frac{x^{2}\cdot \(3\cdot x^{2} +8\cdot x +6 \) }{ 12} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/x,x);} $$\displaylines{\qdd \ln \(x \) \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int((x+1)**3/(x-1)**4,x);} $$\displaylines{\qdd \(3\cdot \ln \(x -1 \) \cdot x^{3} -9\cdot \ln \(x -1 \) \cdot x^{2} +9\cdot \ln \(x -1 \) \cdot x -3\cdot \ln \(x -1 \) -6\cdot x^{3} -2 \) /\nl \(3\cdot \(x^{3} -3\cdot x^{2} +3\cdot x -1 \) \) \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/(x*(x-1)*(x+1)**2),x);} $$\displaylines{\qdd \(\ln \(x -1 \) \cdot x +\ln \(x -1 \) +3\cdot \ln \(x +1 \) \cdot x\nl \off{327680} +3\cdot \ln \(x +1 \) -4\cdot \ln \(x \) \cdot x -4\cdot \ln \(x \) +2\cdot x \) /\nl \(4\cdot \(x +1 \) \) \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int((a*x+b)/((x-p)*(x-q)),x);} $$\displaylines{\qdd \frac{\ln \(p -x \) \cdot a\cdot p +\ln \(p -x \) \cdot b -\ln \(q -x \) \cdot a\cdot q -\ln \(q -x \) \cdot b}{ p -q} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/(a*x**2+b*x+c),x);} $$\displaylines{\qdd \frac{2\cdot \sqrt{4\cdot a\cdot c -b^{2}}\cdot \arctan \(\frac{2\cdot a\cdot x +b}{ \sqrt{4\cdot a\cdot c -b^{2}}} \) }{ 4\cdot a\cdot c -b^{2}} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int((a*x+b)/(1+x**2),x);} $$\displaylines{\qdd \frac{\ln \(x^{2} +1 \) \cdot a +2\cdot \arctan \(x \) \cdot b}{ 2} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/(x**2-2*x+3),x);} $$\displaylines{\qdd \frac{\sqrt{2} \cdot \arctan \(\frac{x -1}{ \sqrt{2}} \) }{ 2} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/((x-1)*(x**2+1))**2,x);} $$\displaylines{\qdd \(\ln \(x^{2} +1 \) \cdot x^{3} -\ln \(x^{2} +1 \) \cdot x^{2} +\ln \(x^{2} +1 \) \cdot x -\ln \(x^{2} +1 \) \nl \off{327680} -2\cdot \ln \(x -1 \) \cdot x^{3} +2\cdot \ln \(x -1 \) \cdot x^{2} -2\cdot \ln \(x -1 \) \cdot x\nl \off{327680} +2\cdot \ln \(x -1 \) +\arctan \(x \) \cdot x^{3} -\arctan \(x \) \cdot x^{2}\nl \off{327680} +\arctan \(x \) \cdot x -\arctan \(x \) -x^{3} -2\cdot x +1 \) /\nl \(4\cdot \(x^{3} -x^{2} +x -1 \) \) \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x/((x-a)*(x-b)*(x-c)),x);} $$\displaylines{\qdd \(\ln \(a -x \) \cdot a\cdot b -\ln \(a -x \) \cdot a\cdot c -\ln \(b -x \) \cdot a\cdot b\nl \off{327680} +\ln \(b -x \) \cdot b\cdot c +\ln \(c -x \) \cdot a\cdot c -\ln \(c -x \) \cdot b\cdot c \) /\nl \(a^{2}\cdot b -a^{2}\cdot c -a\cdot b^{2} +a\cdot c^{2} +b^{2}\cdot c -b\cdot c^{2} \) \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x/((x**2+a**2)*(x**2+b**2)),x);} $$\displaylines{\qdd \frac{-\ln \(a^{2} +x^{2} \) +\ln \(b^{2} +x^{2} \) }{ 2\cdot \(a^{2} -b^{2} \) } \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x**2/((x**2+a**2)*(x**2+b**2)),x);} $$\displaylines{\qdd \frac{\arctan \(\frac{x}{ a} \) \cdot a -\arctan \(\frac{x}{ b} \) \cdot b}{ a^{2} -b^{2}} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x/((x-1)*(x**2+1)),x);} $$\displaylines{\qdd \frac{-\ln \(x^{2} +1 \) +2\cdot \ln \(x -1 \) +2\cdot \arctan \(x \) }{ 4} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x/(1+x**3),x);} $$\displaylines{\qdd \frac{2\cdot \sqrt{3}\cdot \arctan \(\frac{2\cdot x -1}{ \sqrt{3}} \) +\ln \(x^{2} -x +1 \) -2\cdot \ln \(x +1 \) }{ 6} \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x**3/((x-1)**2*(x**3+1)),x);} $$\displaylines{\qdd \(- \(4\cdot \ln \(x^{2} -x +1 \) \cdot x \) +4\cdot \ln \(x^{2} -x +1 \) \nl \off{327680} +9\cdot \ln \(x -1 \) \cdot x -9\cdot \ln \(x -1 \) -\ln \(x +1 \) \cdot x +\ln \(x +1 \) -6\cdot x \) /\nl \(12\cdot \(x -1 \) \) \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/(1+x**4),x);} $$\displaylines{\qdd \(\sqrt{2}\cdot \(-\ln \(- \(\sqrt{2}\cdot x \) +x^{2} +1 \) +\ln \(\sqrt{2}\cdot x +x^{2} +1 \) \nl \off{1277951} -2\cdot \arctan \(\frac{\sqrt{2} -2\cdot x}{ \sqrt{2}} \) +2\cdot \arctan \(\frac{\sqrt{2} +2\cdot x}{ \sqrt{2}} \) \) \) /8 \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x**2/(1+x**4),x);} $$\displaylines{\qdd \(\sqrt{2}\cdot \(\ln \(- \(\sqrt{2}\cdot x \) +x^{2} +1 \) -\ln \(\sqrt{2}\cdot x +x^{2} +1 \) \nl \off{1277951} -2\cdot \arctan \(\frac{\sqrt{2} -2\cdot x}{ \sqrt{2}} \) +2\cdot \arctan \(\frac{\sqrt{2} +2\cdot x}{ \sqrt{2}} \) \) \) /8 \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(1/(1+x**2+x**4),x);} $$\displaylines{\qdd \(2\cdot \sqrt{3}\cdot \arctan \(\frac{2\cdot x -1}{ \sqrt{3}} \) +2\cdot \sqrt{3}\cdot \arctan \(\frac{2\cdot x +1}{ \sqrt{3}} \) \nl \off{327680} -3\cdot \ln \(x^{2} -x +1 \) +3\cdot \ln \(x^{2} +x +1 \) \) /12 \Nl}$$ \TRIexa{Integration}{TeXindent}{1000}{int(sin x**2/x,x);} $$\displaylines{\qdd \int \frac{\sin \(x \) ^{2}}{ x}\,dx \cr}$$ \TRIexa{Integration}{TeXindent}{1000}{int(x*cos(xi/sin(x))*cos(x)/sin(x)**2,x);} $$\displaylines{\qdd \int \frac{\cos \(\frac{\xi }{ \sin \(x \) } \) \cdot \cos \(x \) \cdot x}{ \sin \(x \) ^{2}}\,dx \cr}$$