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# Edit detail for FriCASTimofeev37 revision 1 of 1

 1 Editor: test1 Time: 2013/07/02 00:14:41 GMT+0 Note:

changed:
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Examples from Timofeev Chapter 3 and Chapter 7

\begin{axiom}

INT ==> integrate
pi := %pi
SIN ==> sin
COS ==> cos
TAN ==> tan
COT ==> cot
SEC ==> sec
CSC ==> csc

LN ==> log
SQRT ==> sqrt

ATAN ==> atan
ACOS ==> acos
ASIN ==> asin
ATANH ==> atanh

)boot $IOindex := 1 -- " Timofeev (1948) Ch. 3, examples 1 - 3 (p. 101) ... " INT(1/((x-2)^3*(x+1)^2),x) INT(1/((x+2)^3*(x+3)^4),x) INT(x^5/(3+x)^2,x) -- " Timofeev (1948) Ch. 3, examples 4 - 9 (p. 105) ... " [] [] INT(x/(3+6*x+2*x^2),x) INT((2*x-3)/(3+6*x+2*x^2)^3,x) INT((x-1)/(x^2+5*x+4)^2,x) INT(1/(x^2+3*x+2)^5,x) INT(1/(x^3*(7-6*x+2*x^2)^2),x) INT(x^9/(x^2+3*x+2)^5,x) INT((1+2*x)^2/(3+5*x+2*x^2)^5,x) -- " Timofeev (1948) Ch. 3, examples 13 - 14 (p. 113) ... " INT((a-b*x^2)^3/x^7,x) INT(x^13/(a^4+x^4)^5,x) -- " ... end of Timofeev Ch. 3 " )boot$IOindex := 1

-- " Timofeev (1948) Ch. 7, examples 1 - 4 (p. 334) ... "

INT(x^2*COS(x)^5,x)

INT(x^3*SIN(x)^3,x)

INT(x^2*SIN(x)^6,x)

INT(x^2*SIN(x)^2*COS(x),x)

-- " Timofeev (1948) Ch. 7, examples 5 - 9 (p. 342-343) ... "

INT(x*COS(x)^4/SIN(x)^2,x)

INT(x*SIN(x)^3/COS(x)^4,x)

INT(x*SIN(x)/COS(x)^3,x)

INT(x*SIN(x)^3/COS(x),x)

INT(x*SIN(x)^3/COS(x)^3,x)

-- " Timofeev (1948) Ch. 7, examples 10 - 11 (p. 344) ... "

INT((2*x+SIN(2*x))/(x*SIN(x)+COS(x))^2,x)

INT((x/(x*COS(x)-SIN(x)))^2,x)

-- " ... end of Timofeev Ch. 7 "

\end{axiom}


Examples from Timofeev Chapter 3 and Chapter 7

fricas
INT ==> integrate
Type: Void
fricas
pi := %pi
 (1)
Type: Pi
fricas
SIN ==> sin
Type: Void
fricas
COS ==> cos
Type: Void
fricas
TAN ==> tan
Type: Void
fricas
COT ==> cot
Type: Void
fricas
SEC ==> sec
Type: Void
fricas
CSC ==> csc
Type: Void
fricas
LN ==> log
Type: Void
fricas
SQRT ==> sqrt
Type: Void
fricas
ATAN ==> atan
Type: Void
fricas
ACOS ==> acos
Type: Void
fricas
ASIN ==> asin
Type: Void
fricas
ATANH ==> atanh
Type: Void
fricas
)boot $IOindex := 1 (EVAL-WHEN (EVAL LOAD) (SETQ |$IOindex| 1))
Value = 1
-- " Timofeev (1948) Ch. 3, examples 1 - 3 (p. 101) ... "
INT(1/((x-2)^3*(x+1)^2),x)
 (2)
Type: Union(Expression(Integer),...)
fricas
INT(1/((x+2)^3*(x+3)^4),x)
 (3)
Type: Union(Expression(Integer),...)
fricas
INT(x^5/(3+x)^2,x)
 (4)
Type: Union(Expression(Integer),...)
fricas
-- " Timofeev (1948) Ch. 3, examples 4 - 9 (p. 105) ... "
[]
 (5)
Type: List(None)
fricas
[]
 (6)
Type: List(None)
fricas
INT(x/(3+6*x+2*x^2),x)
 (7)
Type: Union(Expression(Integer),...)
fricas
INT((2*x-3)/(3+6*x+2*x^2)^3,x)
 (8)
Type: Union(Expression(Integer),...)
fricas
INT((x-1)/(x^2+5*x+4)^2,x)
 (9)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x^2+3*x+2)^5,x)
 (10)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x^3*(7-6*x+2*x^2)^2),x)
 (11)
Type: Union(Expression(Integer),...)
fricas
INT(x^9/(x^2+3*x+2)^5,x)
 (12)
Type: Union(Expression(Integer),...)
fricas
INT((1+2*x)^2/(3+5*x+2*x^2)^5,x)
 (13)
Type: Union(Expression(Integer),...)
fricas
-- " Timofeev (1948) Ch. 3, examples 13 - 14 (p. 113) ... "
INT((a-b*x^2)^3/x^7,x)
 (14)
Type: Union(Expression(Integer),...)
fricas
INT(x^13/(a^4+x^4)^5,x)
 (15)
Type: Union(Expression(Integer),...)
fricas
-- " ... end of Timofeev Ch. 3 "

fricas
)boot $IOindex := 1 (EVAL-WHEN (EVAL LOAD) (SETQ |$IOindex| 1))
Value = 1
-- " Timofeev (1948) Ch. 7, examples 1 - 4 (p. 334) ... "
INT(x^2*COS(x)^5,x)
 (16)
Type: Union(Expression(Integer),...)
fricas
INT(x^3*SIN(x)^3,x)
 (17)
Type: Union(Expression(Integer),...)
fricas
INT(x^2*SIN(x)^6,x)
 (18)
Type: Union(Expression(Integer),...)
fricas
INT(x^2*SIN(x)^2*COS(x),x)
 (19)
Type: Union(Expression(Integer),...)
fricas
-- " Timofeev (1948) Ch. 7, examples 5 - 9 (p. 342-343) ... "
INT(x*COS(x)^4/SIN(x)^2,x)
 (20)
Type: Union(Expression(Integer),...)
fricas
INT(x*SIN(x)^3/COS(x)^4,x)
 (21)
Type: Union(Expression(Integer),...)
fricas
INT(x*SIN(x)/COS(x)^3,x)
 (22)
Type: Union(Expression(Integer),...)
fricas
INT(x*SIN(x)^3/COS(x),x)
dilog
[- sin(x) + 1 + cos(x)%i]
 (23)
Type: Union(Expression(Integer),...)
fricas
INT(x*SIN(x)^3/COS(x)^3,x)
dilog
[- sin(x) + 1 + cos(x)%i]
 (24)
Type: Union(Expression(Integer),...)
fricas
-- " Timofeev (1948) Ch. 7, examples 10 - 11 (p. 344) ... "
INT((2*x+SIN(2*x))/(x*SIN(x)+COS(x))^2,x)
 (25)
Type: Union(Expression(Integer),...)
fricas
INT((x/(x*COS(x)-SIN(x)))^2,x)
 (26)
Type: Union(Expression(Integer),...)