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Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

 Messages: [ Previous | Next ]
 Axel Vogt Posts: 1,068 Registered: 5/5/07
Re: An independent integration test suite
Posted: Apr 20, 2013 2:05 PM

It is not lack of interest ...

Here in Maple syntax (hopefull translated correctly, but I modified
muliple identities). Have not yet checked all (already the first is
not directly 'true' in Maple):

Int(1/(-b^2*x^2+a^2),x) =
1/a/b*arctanh(b*x/a)

Int(1/(b^2*x^2+a^2),x) =
1/a/b*arctan(b*x/a)

Int(sec(2*a*x),x) =
-1/2/a*ln(cot(1/4*Pi+a*x))

Int(1/4/sin(1/3*x),x) =
3/8*ln((1-cos(1/3*x))/(1+cos(1/3*x)))

Int(-1/cos(1/4*Pi+2*x),x) =
1/2*ln(cot(3/8*Pi+x))

Int(sec(x)*tan(x),x) =
sec(x)

Int(csc(x)*cot(x),x) =
-csc(x)

Int(tan(x)/sin(2*x),x) =
1/2*tan(x)

Int(1/(1+cos(x)),x) =
tan(1/2*x)

Int(1/(1-cos(x)),x) =
-cot(1/2*x)

Int(sin(x)/(a-b*cos(x)),x) =
1/b*ln(a-b*cos(x))

Int(cos(x)/(a^2+b^2*sin(x)^2),x) =
1/a/b*arctan(b*sin(x)/a)

Int(cos(x)/(a^2-b^2*sin(x)^2),x) =
1/a/b*arctanh(b*sin(x)/a)

Int(sin(2*x)/(a^2+b^2*sin(x)^2),x) =
1/b^2*ln(a^2+b^2*sin(x)^2)

Int(sin(2*x)/(b^2*sin(x)^2-a^2),x) =
1/b^2*ln(a^2-b^2*sin(x)^2)

Int(sin(2*x)/(cos(x)^2*b^2+a^2),x) =
-1/b^2*ln(cos(x)^2*b^2+a^2)

Int(sin(2*x)/(cos(x)^2*b^2-a^2),x) =
-1/b^2*ln(a^2-cos(x)^2*b^2)

Int(1/(4-cos(x)^2),x) =
1/6*3^(1/2)*(arctan(sin(x)*cos(x)/(2*3^(1/2)+4-cos(x)^2))+x)

Int(exp(x)/(exp(2*x)-1),x) =
-arctanh(exp(x))

Int(1/x/ln(x),x) =
ln(ln(x))

Int(1/x/(1+ln(x)^2),x) =
arctan(ln(x))

Int(1/x/(1-ln(x)),x) =
-ln(1-ln(x))

Int(1/x/(1+ln(x/a)),x) =
ln(1+ln(x/a))

Int((1-x^(1/2)+x)^2/x^2,x) =
3*ln(x)+x-4*x^(1/2)+4/x^(1/2)-1/x

Int((2-x^(2/3))*(x+x^(1/2))/x^(3/2),x) =
2*ln(x)-6/7*x^(7/6)-3/2*x^(2/3)+4*x^(1/2)

Int((2*x-1)/(2*x+3),x) =
x-2*ln(2*x+3)

Int((2*x-5)/(3*x^2-2),x) =
1/3*ln(-3*x^2+2)+5/6*6^(1/2)*arctanh(1/2*6^(1/2)*x)

Int((2*x-5)/(3*x^2+2),x) =
1/3*ln(3*x^2+2)-5/6*6^(1/2)*arctan(1/2*6^(1/2)*x)

Int(sin(x)*sin(1/4*x),x) =
2/3*sin(3/4*x)-2/5*sin(5/4*x)

Int(cos(3*x)*cos(4*x),x) =
1/14*sin(7*x)+1/2*sin(x)

Int(-tan(x)*tan(-x+a),x) =
1/tan(a)*ln(1+tan(a)*tan(x))-x

Int(sin(x)^2,x) =
1/2*x-1/2*sin(x)*cos(x)

Int(cos(x)^2,x) =
1/2*x+1/2*sin(x)*cos(x)

Int(sin(x)*cos(x)^3,x) =
-1/4*cos(x)^4

Int(cos(x)^3/sin(x)^4,x) =
1/sin(x)-1/3/sin(x)^3

Int(1/sin(x)^2/cos(x)^2,x) =
tan(x)-cot(x)

Int(cot(3/4*x)^2,x) =
-4/3*cot(3/4*x)-x

Int((1+tan(2*x))^2,x) =
1/2*tan(2*x)-ln(cos(2*x))

Int((tan(x)-cot(x))^2,x) =
tan(x)-cot(x)-4*x

Int((tan(x)-sec(x))^2,x) =
-2*cot(1/2*x+1/4*Pi)-x

Int(sin(x)/(1+sin(x)),x) =
cot(1/2*x+1/4*Pi)+x

Int(cos(x)/(1-cos(x)),x) =
-cot(1/2*x)-x

Int((exp(1/2*x)-1)^3*exp(-1/2*x),x) =
-6*exp(1/2*x)+2*exp(-1/2*x)+exp(x)+3*x

Int(1/(x^2-6*x+5),x) =
1/4*ln((x-5)/(x-1))

Int(x^2/(x^6-6*x^3+13),x) =
1/6*arctan(1/2*x^3-3/2)

Int((x+2)/(x^2-4*x-1),x) =
1/10*(4*5^(1/2)+5)*ln(x-5^(1/2)-2)+1/10*(5-4*5^(1/2))*ln(x+5^(1/2)-2)

Int(1/(1+(x+1)^(1/3)),x) =
3/2*(x+1)^(2/3)-3*(x+1)^(1/3)+3*ln(1+(x+1)^(1/3))

Int(1/(a*x+b)/x^(1/2),x) =
2/a^(1/2)/b^(1/2)*arctan(a^(1/2)*x^(1/2)/b^(1/2))

Int(x^3*(x^2+1)^(1/2),x) =
1/15*(3*x^4+x^2-2)*(x^2+1)^(1/2)

Int(x/(a^4-x^4)^(1/2),x) =
1/2*arcsin(x^2/a^2)

Int(1/x/(-a^2+x^2)^(1/2),x) =
1/a*arctan((-a^2+x^2)^(1/2)/a)

Int(1/x/(a^2-x^2)^(1/2),x) =
-1/a*arctanh((a^2-x^2)^(1/2)/a)

Int(1/x/(a^2+x^2)^(1/2),x) =
-1/a*arctanh(a/(a^2+x^2)^(1/2))

Int(1/(-x^2+x+2)^(1/2),x) =
arcsin(2/3*x-1/3)

Int(1/(3*x^2-4*x+5)^(1/2),x) =
1/3*3^(1/2)*ln(3^(1/2)*(3*x^2-4*x+5)^(1/2)+3*x-2)

Int(1/(-x^2+x)^(1/2),x) =
arcsin(2*x-1)

Int((2*x+1)/(-x^2+x+2)^(1/2),x) =
2*arcsin(2/3*x-1/3)-2*(-x^2+x+2)^(1/2)

Int(1/x/(-x^2+x+2)^(1/2),x) =
1/2*2^(1/2)*ln((2*2^(1/2)*(-x^2+x+2)^(1/2)-x-4)/x)

Int(1/(x-2)/(-x^2+x+2)^(1/2),x) =
2*(-x^2+x+2)^(1/2)/(3*x-6)

Int((2+3*sin(x))/sin(x)/(1-cos(x)),x) =
1/2*ln((1-cos(x))/(1+cos(x)))+(3*sin(x)+1)/(cos(x)-1)

Int(1/(2+3*cos(x)^2),x) =
1/10*10^(1/2)*(x-arctan(3*sin(x)*cos(x)/(10^(1/2)+2+3*cos(x)^2)))

Int((1-tan(x))/sin(2*x),x) =
1/2*ln(tan(x))-1/2*tan(x)

Int((1+tan(x)^2)/(1-tan(x)^2),x) =
1/2*ln((tan(x)+1)/(1-tan(x)))

Int((a^2-4*cos(x)^2)^(3/4)*sin(2*x),x) =
1/7*(a^2-4*cos(x)^2)^(7/4)

Int(sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x) =
-3/8*(a^2-4*sin(x)^2)^(2/3)

Int(1/(a^(2*x)-1)^(1/2),x) =
1/ln(a)*arctan((a^(2*x)-1)^(1/2))

Int(exp(1/2*x)/(exp(x)-1)^(1/2),x) =
2*ln((exp(x)-1)^(1/2)+exp(1/2*x))

Int(arctan(x)^n/(x^2+1),x) =
1/(n+1)*arctan(x)^(n+1)

Int(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x) =
2/5*a/(a^2-x^2)^(1/2)*(1-x^2/a^2)^(1/2)*arcsin(x/a)^(5/2)

Int(1/arccos(x)^3/(-x^2+1)^(1/2),x) =
1/2/arccos(x)^2

Int(ln(x)^2*x,x) =
1/2*x^2*(ln(x)^2-ln(x)+1/2)

Int(ln(x)/x^5,x) =
-1/16*(4*ln(x)+1)/x^4

Int(x^2*ln((x-1)/x),x) =
1/3*x^3*ln((x-1)/x)-1/3*ln(x-1)-1/6*x*(x+2)

Int(cos(x)^5,x) =
1/15*sin(x)*(3*cos(x)^4+4*cos(x)^2+8)

Int(cos(x)^4*sin(x)^2,x) =
1/6*sin(x)^3*cos(x)^3+1/8*sin(x)^3*cos(x)-1/16*sin(x)*cos(x)+1/16*x

Int(1/sin(x)^5,x) =
3/16*ln((1-cos(x))/(1+cos(x)))-3/8*cos(x)/sin(x)^2-1/4*cos(x)/sin(x)^4

Int(sin(x)*exp(-x),x) =
-1/2*(cos(x)+sin(x))*exp(-x)

Int(exp(2*x)*sin(3*x),x) =
1/13*exp(2*x)*(2*sin(3*x)-3*cos(3*x))

Int(a^x*cos(x),x) =
a^x/(ln(a)^2+1)*(ln(a)*cos(x)+sin(x))

Int(cos(ln(x)),x) =
1/2*x*(cos(ln(x))+sin(ln(x)))

Int(sec(x)^2*ln(cos(x)),x) =
tan(x)*ln(cos(x))+tan(x)-x

Int(x*tan(x)^2,x) =
ln(cos(x))+x*tan(x)-1/2*x^2

Int(arcsin(x)/x^2,x) =
-arcsin(x)/x+ln((1-(-x^2+1)^(1/2))/x)

Int(arcsin(x)^2,x) =
x*arcsin(x)^2+2*arcsin(x)*(-x^2+1)^(1/2)-2*x

Int(x^2*arctan(x)/(x^2+1),x) =
x*arctan(x)-1/2*arctan(x)^2-1/2*ln(x^2+1)

Int(arccos((x/(x+1))^(1/2)),x) =
(x+1)*(arccos((x/(x+1))^(1/2))+(1/(x+1))^(1/2)*(x/(x+1))^(1/2))

Date Subject Author
2/24/13 clicliclic@freenet.de
3/19/13 clicliclic@freenet.de
3/21/13 Waldek Hebisch
3/22/13 clicliclic@freenet.de
3/26/13 Waldek Hebisch
3/26/13 clicliclic@freenet.de
4/20/13 clicliclic@freenet.de
4/20/13 Nasser Abbasi
4/20/13 Rouben Rostamian
4/20/13 clicliclic@freenet.de
4/20/13 Rouben Rostamian
4/20/13 Axel Vogt
4/20/13 clicliclic@freenet.de
4/20/13 Axel Vogt
4/21/13 Axel Vogt
4/21/13 clicliclic@freenet.de
4/21/13 Waldek Hebisch
4/22/13 clicliclic@freenet.de
4/22/13 Axel Vogt
4/22/13 clicliclic@freenet.de
4/23/13 Waldek Hebisch
4/24/13 clicliclic@freenet.de
4/25/13 Waldek Hebisch
4/26/13 clicliclic@freenet.de
4/27/13 Waldek Hebisch
4/24/13 Richard Fateman
4/24/13 clicliclic@freenet.de
4/25/13 Richard Fateman
4/26/13 clicliclic@freenet.de
4/26/13 Axel Vogt
4/27/13 clicliclic@freenet.de
4/25/13 Waldek Hebisch
4/25/13 Peter Pein
4/25/13 Nasser Abbasi
4/26/13 Peter Pein
4/26/13 clicliclic@freenet.de
4/26/13 Peter Pein
4/26/13 clicliclic@freenet.de
4/26/13 Richard Fateman
4/27/13 clicliclic@freenet.de
4/27/13 Richard Fateman
6/30/13 clicliclic@freenet.de
6/30/13 Axel Vogt
7/1/13 clicliclic@freenet.de
7/1/13 Axel Vogt
7/1/13 Waldek Hebisch
7/2/13 clicliclic@freenet.de
7/2/13 clicliclic@freenet.de
7/2/13 clicliclic@freenet.de
7/2/13 Nasser Abbasi
7/2/13 Nasser Abbasi
7/4/13 clicliclic@freenet.de
7/4/13 Nasser Abbasi
7/4/13 Nasser Abbasi
7/5/13 clicliclic@freenet.de
7/5/13 Nasser Abbasi
7/9/13 clicliclic@freenet.de
7/10/13 Nasser Abbasi
7/10/13 Richard Fateman
7/10/13 Nasser Abbasi
7/10/13 clicliclic@freenet.de
8/6/13 clicliclic@freenet.de
9/15/13 Albert D. Rich
9/15/13 clicliclic@freenet.de
9/15/13 clicliclic@freenet.de
9/21/13 Albert D. Rich
9/21/13 clicliclic@freenet.de
9/22/13 daly@axiom-developer.org
9/24/13 daly@axiom-developer.org
9/30/13 daly@axiom-developer.org
9/22/13 Albert D. Rich
9/25/13 Albert D. Rich
9/25/13 Albert D. Rich
9/25/13 clicliclic@freenet.de
9/25/13 Albert D. Rich
9/26/13 Albert D. Rich
9/26/13 clicliclic@freenet.de
9/26/13 Albert D. Rich
9/29/13 clicliclic@freenet.de
10/1/13 Albert D. Rich
10/1/13 clicliclic@freenet.de
10/1/13 Albert D. Rich
10/5/13 clicliclic@freenet.de
10/5/13 Albert D. Rich
10/6/13 clicliclic@freenet.de
10/10/13 Albert D. Rich
10/10/13 Nasser Abbasi
10/11/13 clicliclic@freenet.de
11/6/13 Albert D. Rich
11/6/13 Nasser Abbasi
11/7/13 did
11/7/13 clicliclic@freenet.de
11/7/13 clicliclic@freenet.de
11/7/13 Albert D. Rich
11/12/13 clicliclic@freenet.de
11/12/13 Albert D. Rich
11/13/13 clicliclic@freenet.de
11/13/13 Albert D. Rich
11/14/13 clicliclic@freenet.de
11/14/13 Albert D. Rich
11/15/13 clicliclic@freenet.de
11/15/13 Albert D. Rich
11/16/13 clicliclic@freenet.de
11/16/13 clicliclic@freenet.de
11/21/13 Albert D. Rich
11/21/13 clicliclic@freenet.de
11/21/13 Nasser Abbasi
11/21/13 Albert D. Rich
11/21/13 Albert D. Rich
11/22/13 clicliclic@freenet.de
11/14/13 Albert D. Rich
11/15/13 clicliclic@freenet.de
11/15/13 Nasser Abbasi
11/16/13 clicliclic@freenet.de
11/16/13 Nasser Abbasi
11/7/13 did
11/7/13 clicliclic@freenet.de
4/20/13 Richard Fateman
4/21/13 clicliclic@freenet.de
4/20/13 Axel Vogt
4/20/13 clicliclic@freenet.de
4/20/13 Waldek Hebisch
4/21/13 G. A. Edgar
12/8/13 clicliclic@freenet.de
10/5/13 Albert D. Rich
10/6/13 clicliclic@freenet.de