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Examples from Timofeev (1948) Ch. 1, divided into sections kindly provided by clicliclic vel Martin on sci.math.symbolic

fricas
INT ==> integrate
Type: Void
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pi ==> %pi
Type: Void
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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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-- Timofeev (1948) Ch. 1, examples 1 - 21
INT(1/(a^2-b^2*x^2),x)
 (1)
Type: Union(Expression(Integer),...)
fricas
INT(1/(a^2+b^2*x^2),x)
 (2)
Type: Union(Expression(Integer),...)
fricas
INT(SEC(2*a*x),x)
 (3)
Type: Union(Expression(Integer),...)
fricas
INT(1/(4*SIN(x/3)),x)
 (4)
Type: Union(Expression(Integer),...)
fricas
INT(1/COS(3/4*pi-2*x),x)
 (5)
Type: Union(Expression(Integer),...)
fricas
INT(SEC(x)*TAN(x),x)
 (6)
Type: Union(Expression(Integer),...)
fricas
INT(CSC(x)*COT(x),x)
 (7)
Type: Union(Expression(Integer),...)
fricas
INT(TAN(x)/SIN(2*x),x)
 (8)
Type: Union(Expression(Integer),...)
fricas
INT(1/(1+COS(x)),x)
 (9)
Type: Union(Expression(Integer),...)
fricas
INT(1/(1-COS(x)),x)
 (10)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)/(a-b*COS(x)),x)
 (11)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)/(a^2+b^2*SIN(x)^2),x)
 (12)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)/(a^2-b^2*SIN(x)^2),x)
 (13)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(2*x)/(b^2*SIN(x)^2+a^2),x)
 (14)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(2*x)/(b^2*SIN(x)^2-a^2),x)
 (15)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(2*x)/(b^2*COS(x)^2+a^2),x)
 (16)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(2*x)/(b^2*COS(x)^2-a^2),x)
 (17)
Type: Union(Expression(Integer),...)
fricas
INT(1/(4-COS(x)^2),x)
 (18)
Type: Union(Expression(Integer),...)
fricas
INT(%e^x/(%e^(2*x)-1),x)
 (19)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*LN(x)),x)
 (20)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*(1+LN(x)^2)),x)
 (21)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*(1-LN(x))),x)
 (22)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*(1+LN(x/a))),x)
 (23)
Type: Union(Expression(Integer),...)
fricas
-- Timofeev (1948) Ch. 1, examples 22 - 40 (p. 27-28)
INT(((1-SQRT(x)+x)/x)^2,x)
 (24)
Type: Union(Expression(Integer),...)
fricas
INT((2-x^(2/3))*(x+SQRT(x))/x^(3/2),x)
 (25)
Type: Union(Expression(Integer),...)
fricas
INT((2*x-1)/(2*x+3),x)
 (26)
Type: Union(Expression(Integer),...)
fricas
INT((2*x-5)/(3*x^2-2),x)
 (27)
Type: Union(Expression(Integer),...)
fricas
INT((2*x-5)/(3*x^2+2),x)
 (28)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)*SIN(x/4),x)
 (29)
Type: Union(Expression(Integer),...)
fricas
INT(COS(3*x)*COS(4*x),x)
 (30)
Type: Union(Expression(Integer),...)
fricas
INT(TAN(x)*TAN(x-a),x)
 (31)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)^2,x)
 (32)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)^2,x)
 (33)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)*COS(x)^3,x)
 (34)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)^3/SIN(x)^4,x)
 (35)
Type: Union(Expression(Integer),...)
fricas
INT(1/(SIN(x)^2*COS(x)^2),x)
 (36)
Type: Union(Expression(Integer),...)
fricas
INT(COT(3/4*x)^2,x)
 (37)
Type: Union(Expression(Integer),...)
fricas
INT((1+TAN(2*x))^2,x)
 (38)
Type: Union(Expression(Integer),...)
fricas
INT((TAN(x)-COT(x))^2,x)
 (39)
Type: Union(Expression(Integer),...)
fricas
INT((TAN(x)-SEC(x))^2,x)
 (40)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)/(1+SIN(x)),x)
 (41)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)/(1-COS(x)),x)
 (42)
Type: Union(Expression(Integer),...)
fricas
INT((%e^(x/2)-1)^3*%e^(-x/2),x)
 (43)
Type: Union(Expression(Integer),...)
fricas
-- Timofeev (1948) Ch. 1, examples 41 - 65 (p. 35-37)
INT(1/(x^2-6*x+5),x)
 (44)
Type: Union(Expression(Integer),...)
fricas
INT(x^2/(13-6*x^3+x^6),x)
 (45)
Type: Union(Expression(Integer),...)
fricas
INT((x+2)/(x^2-4*x-1),x)
 (46)
Type: Union(Expression(Integer),...)
fricas
INT(1/(1+(x+1)^(1/3)),x)
 (47)
Type: Union(Expression(Integer),...)
fricas
INT(1/((a*x+b)*SQRT(x)),x)
 (48)
Type: Union(List(Expression(Integer)),...)
fricas
INT(x^3*SQRT(1+x^2),x)
 (49)
Type: Union(Expression(Integer),...)
fricas
INT(x/SQRT(a^4-x^4),x)
 (50)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*SQRT(x^2-a^2)),x)
 (51)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*SQRT(a^2-x^2)),x)
 (52)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*SQRT(x^2+a^2)),x)
 (53)
Type: Union(Expression(Integer),...)
fricas
INT(1/SQRT(2+x-x^2),x)
 (54)
Type: Union(Expression(Integer),...)
fricas
INT(1/SQRT(3*x^2-4*x+5),x)
 (55)
Type: Union(Expression(Integer),...)
fricas
INT(1/SQRT(x-x^2),x)
 (56)
Type: Union(Expression(Integer),...)
fricas
INT((2*x+1)/SQRT(2+x-x^2),x)
 (57)
Type: Union(Expression(Integer),...)
fricas
INT(1/(x*SQRT(2+x-x^2)),x)
 (58)
Type: Union(Expression(Integer),...)
fricas
INT(1/((x-2)*SQRT(2+x-x^2)),x)
 (59)
Type: Union(Expression(Integer),...)
fricas
INT((2+3*SIN(x))/(SIN(x)*(1-COS(x))),x)
 (60)
Type: Union(Expression(Integer),...)
fricas
INT(1/(2+3*COS(x)^2),x)
 (61)
Type: Union(Expression(Integer),...)
fricas
INT((1-TAN(x))/SIN(2*x),x)
 (62)
Type: Union(Expression(Integer),...)
fricas
INT((1+TAN(x)^2)/(1-TAN(x)^2),x)
 (63)
Type: Union(Expression(Integer),...)
fricas
INT((a^2-4*COS(x)^2)^(3/4)*SIN(2*x),x)
 (64)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(2*x)/(a^2-4*SIN(x)^2)^(1/3),x)
 (65)
Type: Union(Expression(Integer),...)
fricas
INT(1/SQRT(a^(2*x)-1),x)
 (66)
Type: Union(Expression(Integer),...)
fricas
INT(%e^(x/2)/SQRT(%e^x-1),x)
 (67)
Type: Union(Expression(Integer),...)
fricas
INT(ATAN(x)^n/(1+x^2),x)
 (68)
Type: Union(Expression(Integer),...)
fricas
INT(ASIN(x/a)^(3/2)/SQRT(a^2-x^2),x)
 (69)
Type: Union(Expression(Integer),...)
fricas
INT(1/(ACOS(x)^3*SQRT(1-x^2)),x)
 (70)
Type: Union(Expression(Integer),...)
fricas
-- Timofeev (1948) Ch. 1, examples 66 - 81 (p. 41-42)
INT(LN(x)^2*x,x)
 (71)
Type: Union(Expression(Integer),...)
fricas
INT(LN(x)/x^5,x)
 (72)
Type: Union(Expression(Integer),...)
fricas
INT(x^2*LN((x-1)/x),x)
 (73)
Type: Union(Expression(Integer),...)
fricas
INT(COS(x)^5,x)
 (74)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)^2*COS(x)^4,x)
 (75)
Type: Union(Expression(Integer),...)
fricas
INT(1/SIN(x)^5,x)
 (76)
Type: Union(Expression(Integer),...)
fricas
INT(SIN(x)/%e^x,x)
 (77)
Type: Union(Expression(Integer),...)
fricas
INT(%e^(2*x)*SIN(3*x),x)
 (78)
Type: Union(Expression(Integer),...)
fricas
INT(a^x*COS(x),x)
 (79)
Type: Union(Expression(Integer),...)
fricas
INT(COS(LN(x)),x)
 (80)
Type: Union(Expression(Integer),...)
fricas
INT(SEC(x)^2*LN(COS(x)),x)
 (81)
Type: Union(Expression(Integer),...)
fricas
INT(x*TAN(x)^2,x)
 (82)
Type: Union(Expression(Integer),...)
fricas
INT(ASIN(x)/x^2,x)
 (83)
Type: Union(Expression(Integer),...)
fricas
INT(ASIN(x)^2,x)
 (84)
Type: Union(Expression(Integer),...)
fricas
INT(x^2*ATAN(x)/(1+x^2),x)
 (85)
Type: Union(Expression(Integer),...)
fricas
INT(ACOS(SQRT(x/(x+1))),x)
 (86)
Type: Union(Expression(Integer),...)

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