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Examples from Timofeev Chapter 3 and Chapter 7

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

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)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),...)
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INT(x^3*SIN(x)^3,x)
 (17)
Type: Union(Expression(Integer),...)
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INT(x^2*SIN(x)^6,x)
 (18)
Type: Union(Expression(Integer),...)
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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),...)
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INT(x*SIN(x)/COS(x)^3,x)
 (22)
Type: Union(Expression(Integer),...)
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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),...)

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