reduce-historical/r35/lib/tritstx.tex

\TRIexa{Integration}{TeXindent}{1000}{int(1+x+x**2,x);}
$$\displaylines{\qdd
\frac{x\cdot 
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2*(2*x**2+x)**2,x);}
$$\displaylines{\qdd
\frac{x^{5}\cdot 
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x*(x**2+2*x+1),x);}
$$\displaylines{\qdd
\frac{x^{2}\cdot 
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        +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 
  \(x
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  \)
  \cdot x^{2}
  +9\cdot \ln 
  \(x
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  \)
  \cdot x
  -3\cdot \ln 
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  \)
  -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 
  \(x
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  \)
  \cdot x
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  \(x
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  +3\cdot \ln 
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  +3\cdot \ln 
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  \)
  -4\cdot \ln 
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  \cdot x
  -4\cdot \ln 
  \(x
  \)
  +2\cdot x
\)
/\nl 
\(4\cdot 
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\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int((a*x+b)/((x-p)*(x-q)),x);}
$$\displaylines{\qdd
\frac{\ln 
      \(p
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(1/(a*x**2+b*x+c),x);}
$$\displaylines{\qdd
\frac{2\cdot 
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            -b^{2}}\cdot \arctan 
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              +b}{
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                    -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{2\cdot \arctan 
      \(x
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      \cdot b
      +\ln 
      \(x^{2}
        +1
      \)
      \cdot a}{
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\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
\(\arctan 
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  \(x^{2}
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  \cdot x^{2}\nl 
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  \(x
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  \)
  -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
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  \cdot a\cdot b
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  -\ln 
  \(b
    -x
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  \cdot a\cdot b\nl 
  \off{327680}
  +\ln 
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  \)
  \cdot b\cdot c
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  \)
  \cdot a\cdot c
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  \)
  \cdot b\cdot c
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/\nl 
\(a^{2}\cdot b
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  +b^{2}\cdot c
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\)
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/((x**2+a**2)*(x**2+b**2)),x);}
$$\displaylines{\qdd
\frac{-\ln 
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2/((x**2+a**2)*(x**2+b**2)),x);}
$$\displaylines{\qdd
\frac{\arctan 
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/((x-1)*(x**2+1)),x);}
$$\displaylines{\qdd
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      \(x^{2}
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      }{
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x/(1+x**3),x);}
$$\displaylines{\qdd
\frac{2\cdot 
      \sqrt{3}\cdot \arctan 
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        +1
      \)
      -2\cdot \ln 
      \(x
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      \)
      }{
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\cr}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**3/((x-1)**2*(x**3+1)),x);}
$$\displaylines{\qdd
\(-
  \(4\cdot \ln 
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  +4\cdot \ln 
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    -x
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  \)
  \nl 
  \off{327680}
  +9\cdot \ln 
  \(x
    -1
  \)
  \cdot x
  -9\cdot \ln 
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    -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 
  \(-
    \(2\cdot \arctan 
      \(\frac{\sqrt{2}
              -2\cdot x}{
              \sqrt{2}}
      \)
    \)
    +2\cdot \arctan 
    \(\frac{\sqrt{2}
            +2\cdot x}{
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    \)
    \nl 
    \off{1277951}
    -\ln 
    \(-
      \(\sqrt{2}\cdot x
      \)
      +x^{2}
      +1
    \)
    +\ln 
    \(\sqrt{2}\cdot x
      +x^{2}
      +1
    \)
  \)
\)
/8
\Nl}$$
\TRIexa{Integration}{TeXindent}{1000}{int(x**2/(1+x**4),x);}
$$\displaylines{\qdd
\(\sqrt{2}\cdot 
  \(-
    \(2\cdot \arctan 
      \(\frac{\sqrt{2}
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              \sqrt{2}}
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    +2\cdot \arctan 
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    \(\sqrt{2}\cdot x
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  \)
\)
/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 
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  \(\frac{2\cdot x
          +1}{
          \sqrt{3}}
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  \nl 
  \off{327680}
  -3\cdot \ln 
  \(x^{2}
    -x
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  \)
  +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}$$