%%HP: T(3)A(R)F(.);
DIR
  pi.txt
    DIR
      Sinus
"phi phi    sin
0   0	   0
30  \pi/6  1/2
45  \\p"
    END
  INT
    DIR
      Iexp
"I(dx/x)=ln|x|+c
I(a^x*dx)=a^x/ln(a)+C=a^x (hoch a)log e+C
I(e^x*dx)=e^x+C"
      Isin
"I(sin(x)dx)=-cos(x)+C
I(cos(x)dx)=sin(x)+C
I(tan(x)dx)=-ln|cos(x)|+C
I(cot(x)dx)=ln|sin(x)|+C"
      Issin
"I(dx/cos\178(x))=I(1+tan\178(x)dx)=tan(x)+C
I(dx/sin\178(x)()=I(1+sin\178(x)dx)=-cot(x)+C"
      Isinh
"I(sinh(x)dx=cosh(x)+C
I(cosh(x)dx=sinh(x)+C
I(tanh(x)dx=ln|coshx|+C
I(coth(x)dx=ln|sinhx|+C"
      Issinh
"I(dx/cosh\178(x))=I((1-tanh\178(x))dx)=tanh(x)+C
I(dx/sinh\178(x))=I((coth\178(x)-1)dx)=-coth(x)+C"
      Ixx
"I(dx/(1+x\178))=Arctan(X)+C=-Arccot(x)+C
I(dx/(1-x\178))=1/2*ln|(1+x)/(1-x)|+C=artanh(X)+C=arcoth(x)+C"
      IxxW
"I(dx/Sqrt(1+x\178))=ln|x+Sqrt(x\178+1)|+C=arsinh(x)+C
I(dx/Sqrt(1-x\178))=Arcsin(x)+C1=-Arccos(x)+C2
I(dx/Sqrt(x\178-1)=ln|x+Sqrt(x\178-1)|+C=arcosh(x)+C=-arcosh(-x)+C"
      Iquad
"I(dx/(x\178+bx+d))=2/Sqrt(4d-b\178)*Arctan((2x+b)/Sqrt(4d-b\178))+C"
    END
  SINH.1
    DIR
      Addw
"sinh(x+-y)=sinh(x)*cosh(y)+-cosh(x)*sinh(y)
cosh(x+-y)=cosh(x)*cosh(y)+-sinh(x)*sinh(y)
tanh(x+-y)=(tanh(x)+-tanh(y))/(1+-tanh(x)*tanh(y))
coth(x+-y)=(1+-coth(x)*coth(y))/(coth(x)+-coth(y))"
      Dopw
"sinh(2x)=2*sinh(x)*cosh(y)
cosh(2x)=sinh\178(x)+cosh\178(y)
tanh(2x)=2tanh(x)/(1+tanh\178(x))
cot(2x)=(1+coth\178(x))/(2coth(x))"
      Haw
"sinh(x/2)=Sqrt((coshx-1)/2) f\252r x>0, - x<0
cosh(x/2)=Sqrt((coshx+1)/2)
tanh(x/2)=1/coth(x/2)=sinh(x)/(coshx+1)"
      Sumdif
"sinh(x)+-sinh(y)=2*sinh((x+-y)/2)*cosh((x-+y)/2)
cosh(x)+cosh(y)=2*cosh((x+y)/2)*cosh((x-y)/2)
cosh(x)-cosh(y)=2*sinh((x+y)/2)*sinh((x-y)/2)
tanh(x)+-tanh(y)=sinh(x+-y)/(coshx*coshy)
coth(x)+-coth(y)=+-sinh(x+-y)/(sinh(x)*sinh(y)"
    END
  SUM
    DIR
      Addw
"sin(x+-y)=sin(x)*cos(y)+-cos(x)*sin(y)
tan(x+-y)=(tan(x)+-tan(y)/(1-+tan(x)*tan(y))
cos(x+-y)=cos(x)*cos(y)-+sin(x)*sin(y)
cot(x+-y)=(cot(x)*cot(y)-+1)/(cot(y)+-cot(x))"
      Dwink
"sin(2x)=2*sin(x)*cos(x)
cos(2x)=cos\178(x)-sin\178(x)=(1-tan\178(x))/(1+tan\178(x))
tan(2x)=2tan(x)/(1-tan\178(x))=2/(cot(x)-tan(x))
cot(2x)=(cot\178(x)-1)/(2*cot(x))=(cot(x)-tan(x))/2"
      Hwink
"sin(x/2)=+-Sqrt((1-cos(x)/2)
cos(x/2)=+-Sqrt((1+cos(x)/2)
tan(x/2)=+-Sqrt((1-cos(x))/(1+cos(x))=sin(x)/(1+cos(x)=(1-cos(x))/sin(x)
cot(x/2)=+-Sqrt((1+cos(x))/(1-cos(x))"
      ssin
"sin\178x=(1-cos(2x))/2
sin\179x=(3*sin(x)-sin(3x))/4
sin^4=(3-4*cos(2x)+cos(4x))/8"
      ccos
"cos\178x=(1+cos(2x))/2
cos\179x=(3*cos(x)+cos(3x))/4
cos^4=(3+4*cos(2x)+cos(4x))/8"
      Sumdif
"sin(x)+sin(y)=2*sin((x+y)/2)*cos((x-y)/2)
sin(x)-sin(y)=2*cos((x+y)/2)*sin((x-y)/2)
cos(x)+cos(y)=2*cos((x+y)/2)*cos((x-y)/2)
cos(x)-cos(y)=-2*sin((x+y)/2)*sin((x-y)/2)
tan(x)+-tan(y)=sin(x+-y)/(cos(x)*cos(y))
cot(x)+-cot(y)=+-sin(x+-y)/(sin(x)*sin(y))"
      Prosi
"sin(x)*sin(y)=(cos(x-y)-cos(x+y))/2
cos(x)*cos(y)=(cos(x-y)+cos(x+y))/2
sin(x)*cos(y)=(sin(x-y)+sin(x+y))/2
sin(x+y)*sin(x-y)=cos\178y-sin\178x
cos(x+y)*cos(x-y)=cos\178y-sin\178x
tan(x)*tan(y)=(tan(x)+tan(y))/(cot(x)+cot(y))
cot(x)*cot(y)=(cot(x)+cot(y))/(tan(x)+tan(y))
tan(x)*cot(y)=(tan(x)+cot(y))/(cot(x)+tan(y))"
    END
END