$SPAD/src/input danzwill.input

Timothy Daly December 3, 2016

Abstract

Contents

2

1 The original email

Date: Fri, 3 Apr 92 10:58:35 -0500
From: zwilling@world.std.com (Daniel Zwillinger)
To: axiom@watson.ibm.com
Enclosed is my test suite of integrals in MAPLE format.
I would appreciate you running it under AXIOM and returning the
results to me via email.
Thank you.
----------------------------------------------------------
Daniel Zwillinger            email: zwilling@world.std.com
61 Highland Avenue           phone: 617/646-8565
Arlington, MA 02174
Home of: Handbook of Differential Equations
Home of: Handbook of Integration
-----------------------------------------------------------

2 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)spool danzwill.output
)set message test on
)set message auto off
)clear all
)set break resume
--S 1 of 17
i1 := integrate( sin(x), x)
--R
--R
--R   (1)  - cos(x)
--R                                         Type: Union(Expression(Integer),...)
--E 1
--i2 := integrate( sqrt(tan(x)), x)
--S 2 of 17
i3 := integrate( x/(x**3-1),x)

--R
--R
--R                                                                 +-+
--R           +-+     2              +-+                   (2x + 1)\|3
--R        - \|3 log(x  + x + 1) + 2\|3 log(x - 1) + 6atan(------------)
--R                                                              3
--R   (2)  -------------------------------------------------------------
--R                                      +-+
--R                                    6\|3
--R                                         Type: Union(Expression(Integer),...)
--E 2
--S 3 of 17
i4 := integrate( x/sin(x)**2, x)
--R
--R
--R                    sin(x)                     2
--R        sin(x)log(----------) - sin(x)log(----------) - x cos(x)
--R                  cos(x) + 1              cos(x) + 1
--R   (3)  --------------------------------------------------------
--R                                 sin(x)
--R                                         Type: Union(Expression(Integer),...)
--E 3
--S 4 of 17
i5 := integrate( log(x)/sqrt(x+1), x)
--R
--R
--R              +-----+              +-----+                      +-----+
--R   (4)  2log(\|x + 1  + 1) - 2log(\|x + 1  - 1) + (2log(x) - 4)\|x + 1
--R                                         Type: Union(Expression(Integer),...)
--E 4
--S 5 of 17
i6 := integrate( exp(-a*x**2), x)
--R
--R
--R           x       2
--R         ++    - %N a
--R   (5)   |   %e      d%N
--R        ++
--R                                         Type: Union(Expression(Integer),...)
--E 5
--S 6 of 17
i7 := integrate( x/(log(x))**3, x)
--R
--R
--R               2                2          2
--R        4log(x) Ei(2log(x)) - 2x log(x) - x

--R   (6)  ------------------------------------
--R                             2
--R                      2log(x)
--R                                         Type: Union(Expression(Integer),...)
--E 6
--S 7 of 17
i8 := integrate( x/(sqrt(1+x)+sqrt(1-x)),x)
--R
--R
--R                +-----+             +-------+
--R        (x + 1)\|x + 1  + (- x + 1)\|- x + 1
--R   (7)  -------------------------------------
--R                          3
--R                                         Type: Union(Expression(Integer),...)
--E 7
--S 8 of 17
i9 := integrate( 1/(2+cos(x)),x)
--R
--R
--R                +-+
--R               \|3 sin(x)
--R        2atan(-----------)
--R              3cos(x) + 3
--R   (8)  ------------------
--R                +-+
--R               \|3
--R                                         Type: Union(Expression(Integer),...)
--E 8
--S 9 of 17
i10:= integrate( sin(x)/x**2, x)
--R
--R
--R           x
--R         ++  sin(%N)
--R   (9)   |   ------- d%N
--R        ++       2
--R               %N
--R                                         Type: Union(Expression(Integer),...)
--E 9
--S 10 of 17
d1:= integrate( 1/(2+cos(x)),x=0..4*%pi)
--R
--R
--R   (10)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 10

)set mes test off
--S 11 of 17
d2:= integrate( sin(x)/x,x=%minusInfinity..%plusInfinity)
--R
--R   >> Error detected within library code:
--R   integrate: pole in path of integration
--R
--R   Continuing to read the file...
--R
--E 11
)set mes test on
--S 12 of 17
d3:= integrate( x**2/(1+x**3),x=0..%plusInfinity)
--R
--R
--R   (11)   + infinity
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 12
--S 13 of 17
d4:= integrate( exp(-x)/sqrt(x),x=0..%plusInfinity)
--R
--R
--R          _1
--R   (12)  | (-)
--R            2
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 13
--S 14 of 17
d5:= integrate( exp(-x**2)*log(x)**2,x=0..%plusInfinity)
--R
--R
--R          _1             1     _1         1 2
--R         | (-)polygamma(1,-) + | (-)digamma(-)
--R            2             2       2         2
--R   (13)  --------------------------------------
--R                            8
--R                  Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
--E 14
--S 15 of 17
d6:= integrate( exp(-x)*log(x)**2*x**3,x=1..%plusInfinity)
--R
--R
--R   (14)  potentialPole

--R                                         Type: Union(pole: potentialPole,...)
--E 15
--S 16 of 17
d7:= integrate( exp(-x)*x**(1/3),x=1..%plusInfinity)
--R
--R
--R   (15)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 16
--S 17 of 17
d8:= integrate( exp(-x)*x**2/(1-exp(-2*x)),x=0..%plusInfinity)
--R
--R
--R   (16)  potentialPole
--R                                         Type: Union(pole: potentialPole,...)
--E 17
)spool
)lisp (bye)

———-

References^{[1] nothing}

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