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halirutanhalirutan
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Update test suite
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‎0 Independent test suites/Apostol Problems.m

Lines changed: 2 additions & 2 deletions
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@@ -257,7 +257,7 @@
257257
{E^ArcTan[x]/(1 + x^2)^(3/2), x, 1, (E^ArcTan[x]*(1 + x))/(2*Sqrt[1 + x^2])}
258258
{x^2/(1 + x^2)^2, x, 2, -(x/(2*(1 + x^2))) + ArcTan[x]/2}
259259
{E^x/(1 + E^(2*x)), x, 2, ArcTan[E^x]}
260-
{ArcCot[E^x]/E^x, x, 6, -x - ArcCot[E^x]/E^x + (1/2)*Log[1 + E^(2*x)]}
260+
{ArcCot[E^x]/E^x, x, 5, -x - ArcCot[E^x]/E^x + (1/2)*Log[1 + E^(2*x)]}
261261
{((a + x)/(a - x))^(1/2), x, 3, -((a - x)*Sqrt[(a + x)/(a - x)]) + 2*a*ArcTan[Sqrt[(a + x)/(a - x)]]}
262262
{Sqrt[(x - a)*(b - x)], x, 4, (-(1/4))*(a + b - 2*x)*Sqrt[(-a)*b + (a + b)*x - x^2] - (1/8)*(a - b)^2*ArcTan[(a + b - 2*x)/(2*Sqrt[(-a)*b + (a + b)*x - x^2])]}
263263
{1/Sqrt[(x - a)*(b - x)], x, 3, -ArcTan[(a + b - 2*x)/(2*Sqrt[(-a)*b + (a + b)*x - x^2])]}
@@ -343,7 +343,7 @@
343343
{(8*x^3 + 7)/((x + 1)*(2*x + 1)^3), x, 2, -(3/(1 + 2*x)^2) + 3/(1 + 2*x) + Log[1 + x]}
344344
{(4*x^2 + x + 1)/(x^3 - 1), x, 3, 2*Log[1 - x] + Log[1 + x + x^2]}
345345
{x^4/(x^4 + 5*x^2 + 4), x, 4, x - (8/3)*ArcTan[x/2] + ArcTan[x]/3}
346-
{(x + 2)/(x^2 + x), x, 3, 2*Log[x] - Log[1 + x]}
346+
{(x + 2)/(x^2 + x), x, 2, 2*Log[x] - Log[1 + x]}
347347
{1/(x*(x^2 + 1)^2), x, 3, 1/(2*(1 + x^2)) + Log[x] - (1/2)*Log[1 + x^2]}
348348
{1/((x + 1)*(x + 2)^2*(x + 3)^3), x, 2, 1/(2 + x) + 1/(4*(3 + x)^2) + 5/(4*(3 + x)) + (1/8)*Log[1 + x] + 2*Log[2 + x] - (17/8)*Log[3 + x]}
349349

‎0 Independent test suites/Bondarenko Problems.m

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -49,7 +49,7 @@
4949

5050

5151
{Sqrt[1 + Tanh[4*x]], x, 2, ArcTanh[Sqrt[1 + Tanh[4*x]]/Sqrt[2]]/(2*Sqrt[2])}
52-
{Tanh[x]/Sqrt[Exp[2*x] + Exp[x]], x, -13, (2*Sqrt[E^x + E^(2*x)])/E^x - ArcTan[(I - (1 - 2*I)*E^x)/(2*Sqrt[1 + I]*Sqrt[E^x + E^(2*x)])]/Sqrt[1 + I] + ArcTan[(I + (1 + 2*I)*E^x)/(2*Sqrt[1 - I]*Sqrt[E^x + E^(2*x)])]/Sqrt[1 - I]}
52+
{Tanh[x]/Sqrt[Exp[2*x] + Exp[x]], x, -11, (2*Sqrt[E^x + E^(2*x)])/E^x - ArcTan[(I - (1 - 2*I)*E^x)/(2*Sqrt[1 + I]*Sqrt[E^x + E^(2*x)])]/Sqrt[1 + I] + ArcTan[(I + (1 + 2*I)*E^x)/(2*Sqrt[1 - I]*Sqrt[E^x + E^(2*x)])]/Sqrt[1 - I]}
5353
{Sqrt[Sinh[2*x]/Cosh[x]], x, 5, (2*I*Sqrt[2]*EllipticE[Pi/4 - (I*x)/2, 2]*Sqrt[Sinh[x]])/Sqrt[I*Sinh[x]], (2*I*EllipticE[Pi/4 - (I*x)/2, 2]*Sqrt[Sech[x]*Sinh[2*x]])/Sqrt[I*Sinh[x]]}
5454

5555

‎0 Independent test suites/Bronstein Problems.m

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -13,7 +13,7 @@
1313
{Sqrt[x^8 + 1]/(x*(x^8 + 1)), x, 3, (-(1/4))*ArcTanh[Sqrt[1 + x^8]]}
1414
{x/Sqrt[1 - x^3], x, 3, (2*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (2*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])}
1515
{1/(x*Sqrt[1 - x^3]), x, 3, (-(2/3))*ArcTanh[Sqrt[1 - x^3]]}
16-
{x/Sqrt[x^4 + 10*x^2 - 96*x - 71], x, -1, (-(1/8))*Log[(-(x^6 + 15*x^4 - 80*x^3 + 27*x^2 - 528*x + 781))*Sqrt[x^4 + 10*x^2 - 96*x - 71] + x^8 + 20*x^6 - 128*x^5 + 54*x^4 - 1408*x^3 + 3124*x^2 + 10001]}
16+
{x/Sqrt[x^4 + 10*x^2 - 96*x - 71], x, 1, (1/8)*Log[10001 + 3124*x^2 - 1408*x^3 + 54*x^4 - 128*x^5 + 20*x^6 + x^8 + Sqrt[-71 - 96*x + 10*x^2 + x^4]*(781 - 528*x + 27*x^2 - 80*x^3 + 15*x^4 + x^6)]}
1717

1818

1919
(* ::Section::Closed:: *)
@@ -30,7 +30,7 @@
3030
{(Log[x]^2 + 2*x*Log[x] + x^2 + (x + 1)*Sqrt[x + Log[x]])/(x*Log[x]^2 + 2*x^2*Log[x] + x^3), x, -3, Log[x] - 2/Sqrt[x + Log[x]]}
3131

3232
{(2*Log[x]^2 - Log[x] - x^2)/(Log[x]^3 - x^2*Log[x]), x, 6, (-(1/2))*Log[x - Log[x]] + (1/2)*Log[x + Log[x]] + LogIntegral[x]}
33-
(* {Log[1 + E^x]^(1/3)/(1 + Log[1 + E^x]), x, 0, Int[Log[1 + E^x]^(1/3)/(1 + Log[1 + E^x]), x]} *)
33+
(* {Log[1 + E^x]^(1/3)/(1 + Log[1 + E^x]), x, 0, CannotIntegrate[Log[1 + E^x]^(1/3)/(1 + Log[1 + E^x]), x]} *)
3434
(* {((x^2 + 2*x + 1)*Sqrt[x + Log[x]] + (3*x + 1)*Log[x] + 3*x^2 + x)/((x*Log[x] + x^2)*Sqrt[x + Log[x]] + x^2*Log[x] + x^3), x, 0, 2*Sqrt[x + Log[x]] + 2*Log[x + Sqrt[x + Log[x]]]} *)
3535

3636

‎0 Independent test suites/Charlwood Problems.m

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -36,7 +36,7 @@
3636
(*Problem #5*)
3737

3838

39-
{Cos[x]^2/Sqrt[Cos[x]^4 + Cos[x]^2 + 1], x, -4, x/3 + (1/3)*ArcTan[(Cos[x]*(1 + Cos[x]^2)*Sin[x])/(1 + Cos[x]^2*Sqrt[1 + Cos[x]^2 + Cos[x]^4])]}
39+
{Cos[x]^2/Sqrt[Cos[x]^4 + Cos[x]^2 + 1], x, -5, x/3 + (1/3)*ArcTan[(Cos[x]*(1 + Cos[x]^2)*Sin[x])/(1 + Cos[x]^2*Sqrt[1 + Cos[x]^2 + Cos[x]^4])]}
4040

4141

4242
(* ::Subsection::Closed:: *)

‎0 Independent test suites/Hearn Problems.m

Lines changed: 5 additions & 5 deletions
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@@ -65,7 +65,7 @@
6565
{1/(a*x^3-b), x, 6, -(ArcTan[(b^(1/3) + 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) + Log[b^(1/3) - a^(1/3)*x]/(3*a^(1/3)*b^(2/3)) - Log[b^(2/3) + a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(6*a^(1/3)*b^(2/3))}
6666
{1/(x^4-2), x, 3, -(ArcTan[x/2^(1/4)]/(2*2^(3/4))) - ArcTanh[x/2^(1/4)]/(2*2^(3/4))}
6767
{1/(5*x^4-1), x, 3, -(ArcTan[5^(1/4)*x]/(2*5^(1/4))) - ArcTanh[5^(1/4)*x]/(2*5^(1/4))}
68-
{1/(3*x^4+7), x, 9, If[$VersionNumber<9, -(ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4))) + ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4)) - Log[Sqrt[21] - Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)) + Log[Sqrt[21] + Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)), -(ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4))) + ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4)) - Log[Sqrt[7] - Sqrt[2]*21^(1/4)*x + Sqrt[3]*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)) + Log[Sqrt[7] + Sqrt[2]*21^(1/4)*x + Sqrt[3]*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4))]}
68+
{1/(3*x^4+7), x, 9, If[$VersionNumber<9, -(ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4))) + ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4)) - Log[Sqrt[21] - Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)) + Log[Sqrt[21] + Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)), -(ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4))) + ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x]/(2*Sqrt[2]*3^(1/4)*7^(3/4)) - Log[Sqrt[21] - Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4)) + Log[Sqrt[21] + Sqrt[2]*3^(3/4)*7^(1/4)*x + 3*x^2]/(4*Sqrt[2]*3^(1/4)*7^(3/4))]}
6969
{1/(x^4+3*x^2-1), x, 3, (-Sqrt[2/(13*(3 + Sqrt[13]))])*ArcTan[Sqrt[2/(3 + Sqrt[13])]*x] - Sqrt[(1/26)*(3 + Sqrt[13])]*ArcTanh[Sqrt[2/(-3 + Sqrt[13])]*x]}
7070
{1/(x^4-3*x^2-1), x, 3, (-Sqrt[(1/26)*(3 + Sqrt[13])])*ArcTan[Sqrt[2/(-3 + Sqrt[13])]*x] - Sqrt[2/(13*(3 + Sqrt[13]))]*ArcTanh[Sqrt[2/(3 + Sqrt[13])]*x]}
7171
{1/(x^4-3*x^2+1), x, 3, (-Sqrt[2/(5*(3 + Sqrt[5]))])*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x] + Sqrt[(1/10)*(3 + Sqrt[5])]*ArcTanh[Sqrt[(1/2)*(3 + Sqrt[5])]*x]}
@@ -98,7 +98,7 @@
9898
{1/(x*Log[x]), x, 2, Log[Log[x]]}
9999
{1/(x*Log[x])^2, x, 3, -ExpIntegralEi[-Log[x]] - 1/(x*Log[x])}
100100
{(Log[x])^p/x, x, 2, Log[x]^(1 + p)/(1 + p)}
101-
{Log[x]*(a*x+b), x, 2, (-b)*x - (a*x^2)/4 + (1/2)*(2*b*x + a*x^2)*Log[x]}
101+
{Log[x]*(a*x+b), x, 2, (-b)*x - (a*x^2)/4 + b*x*Log[x] + (1/2)*a*x^2*Log[x]}
102102
{(a*x+b)^2*Log[x], x, 4, (-b^2)*x - (1/2)*a*b*x^2 - (a^2*x^3)/9 - (b^3*Log[x])/(3*a) + ((b + a*x)^3*Log[x])/(3*a)}
103103
{Log[x]/(a*x+b)^2, x, 2, (x*Log[x])/(b*(b + a*x)) - Log[b + a*x]/(a*b)}
104104
{x*Log[a*x+b], x, 3, (b*x)/(2*a) - x^2/4 - (b^2*Log[b + a*x])/(2*a^2) + (1/2)*x^2*Log[b + a*x]}
@@ -238,7 +238,7 @@
238238
(* Examples involving exponentials and logarithms. *)
239239
{E^x*Log[x], x, 2, -ExpIntegralEi[x] + E^x*Log[x]}
240240
{x*E^x*Log[x], x, 5, -E^x + ExpIntegralEi[x] - E^x*Log[x] + E^x*x*Log[x]}
241-
{E^(2*x)*Log[E^x], x, 2, -(E^(2*x)/4) + (1/2)*E^(2*x)*Log[E^x]}
241+
{E^(2*x)*Log[E^x], x, 3, -(E^(2*x)/4) + (1/2)*E^(2*x)*Log[E^x]}
242242

243243

244244
(* ::Section::Closed:: *)
@@ -397,7 +397,7 @@
397397

398398
(* The next integral appeared in Risch's 1968 paper. *)
399399

400-
{2*x*E^(x^2)*Log[x]+E^(x^2)/x+(Log[x]-2)/(Log[x]^2+x)^2+((2/x)*Log[x]+(1/x)+1)/(Log[x]^2+x), x, -9, E^x^2*Log[x] - Log[x]/(x + Log[x]^2) + Log[x + Log[x]^2]}
400+
{2*x*E^(x^2)*Log[x]+E^(x^2)/x+(Log[x]-2)/(Log[x]^2+x)^2+((2/x)*Log[x]+(1/x)+1)/(Log[x]^2+x), x, 9, E^x^2*Log[x] - Log[x]/(x + Log[x]^2) + Log[x + Log[x]^2]}
401401

402402

403403
(* The following integral would not evaluate in REDUCE 3.3. *)
@@ -429,7 +429,7 @@
429429

430430
(* This used to reveal bugs in the integrator which have been fixed. *)
431431

432-
{Sqrt[-4*Sqrt[2] + 9]*x - Sqrt[x^4 + 2*x^2 + 4*x + 1]*Sqrt[2], x, 1, (1/2)*Sqrt[9 - 4*Sqrt[2]]*x^2 - Sqrt[2]*CannotIntegrate[Sqrt[1 + 4*x + 2*x^2 + x^4], x]}
432+
{Sqrt[-4*Sqrt[2] + 9]*x - Sqrt[x^4 + 2*x^2 + 4*x + 1]*Sqrt[2], x, -1, (1/2)*Sqrt[9 - 4*Sqrt[2]]*x^2 - Sqrt[2]*((-(1/3))*Sqrt[1 + 4*x + 2*x^2 + x^4] + (1/3)*(1 + x)*Sqrt[1 + 4*x + 2*x^2 + x^4] + (4*I*(-13 + 3*Sqrt[33])^(1/3)*Sqrt[1 + 4*x + 2*x^2 + x^4])/(4*2^(2/3)*(-I + Sqrt[3]) - 2*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3) + 6*I*(-13 + 3*Sqrt[33])^(1/3)*x) - (8*2^(2/3)*Sqrt[3/(-13 + 3*Sqrt[33] + 4*(-26 + 6*Sqrt[33])^(1/3))]*Sqrt[(I*(-19899 + 3445*Sqrt[33] + (-26 + 6*Sqrt[33])^(2/3)*(-2574 + 466*Sqrt[33]) + (-26 + 6*Sqrt[33])^(1/3)*(-19899 + 3445*Sqrt[33]) + (59697 - 10335*Sqrt[33])*x))/((-39 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 9*Sqrt[33] + 4*I*(3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))*(26 - 6*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x))]*Sqrt[1 + 4*x + 2*x^2 + x^4]*EllipticE[ArcSin[Sqrt[26 - 6*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x]/(Sqrt[(39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] - 9*Sqrt[33] + 4*(3 - I*Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))/(39 - 13*I*Sqrt[3] + 9*I*Sqrt[11] - 9*Sqrt[33] + 4*(3 + I*Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))]*Sqrt[26 - 6*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x])], (4*(21 + 7*I*Sqrt[3] - 3*I*Sqrt[11] - 3*Sqrt[33]) + (3 - I*Sqrt[3] - 3*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3))/(4*(21 - 7*I*Sqrt[3] + 3*I*Sqrt[11] - 3*Sqrt[33]) + (3 + I*Sqrt[3] + 3*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3))])/((4*2^(2/3) - (-13 + 3*Sqrt[33])^(1/3) - 2^(1/3)*(-13 + 3*Sqrt[33])^(2/3) + 3*(-13 + 3*Sqrt[33])^(1/3)*x)*Sqrt[(I*(1 + x))/((104 - 24*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3))*(26 - 6*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x))]*Sqrt[26 - 6*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x]*Sqrt[26 - 6*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x]) + ((2^(1/3)*(13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] - 3*Sqrt[33]) + 4*2^(2/3)*(1 + I*Sqrt[3])*(-13 + 3*Sqrt[33])^(1/3) + 20*(-13 + 3*Sqrt[33])^(2/3))*(4*2^(2/3)*(I + Sqrt[3]) + 8*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(-I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3))*Sqrt[(52 - 12*Sqrt[33] - 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) + 4*(-26 + 6*Sqrt[33])^(2/3))/(-13 + 3*Sqrt[33] + 4*(-26 + 6*Sqrt[33])^(1/3))]*Sqrt[(1/(1 + x))*(-8*I*(-13 + 3*Sqrt[33]) + (-43*I - 13*Sqrt[3] + 9*Sqrt[11] + 5*I*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (2*I + 4*Sqrt[3] - 2*I*Sqrt[33])*(-26 + 6*Sqrt[33])^(2/3) + (8*I*(-13 + 3*Sqrt[33]) + (13*I - 13*Sqrt[3] + 9*Sqrt[11] - 3*I*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3))*x)]*Sqrt[1 + 4*x + 2*x^2 + x^4]*EllipticF[ArcSin[(Sqrt[52 - 12*Sqrt[33] - 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) + 4*(-26 + 6*Sqrt[33])^(2/3)]*Sqrt[26 - 6*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x])/(2^(1/6)*Sqrt[3]*(-13 + 3*Sqrt[33])^(2/3)*Sqrt[39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] - 9*Sqrt[33] + 4*(3 - I*Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3)]*Sqrt[1 + x])], (4*(21*I - 7*Sqrt[3] + 3*Sqrt[11] - 3*I*Sqrt[33]) + (3*I + Sqrt[3] + 3*Sqrt[11] + 3*I*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3))/(-56*Sqrt[3] + 24*Sqrt[11] + 2*(Sqrt[3] + 3*Sqrt[11])*(-26 + 6*Sqrt[33])^(1/3))])/(3*2^(2/3)*3^(3/4)*(-13 + 3*Sqrt[33])^(1/3)*Sqrt[39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] - 9*Sqrt[33] + 4*(3 - I*Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3)]*Sqrt[1 + x]*(4*2^(2/3)*(-I + Sqrt[3]) - 2*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3) + 6*I*(-13 + 3*Sqrt[33])^(1/3)*x)*Sqrt[26 - 6*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3) + 6*(-13 + 3*Sqrt[33])*x]*Sqrt[(8*(-13 + 3*Sqrt[33]) - (5 - 3*I*Sqrt[3] + 3*I*Sqrt[11] + Sqrt[33])*(-26 + 6*Sqrt[33])^(2/3) + (-26 + 6*Sqrt[33])^(1/3)*(-41 + 15*I*Sqrt[3] - 3*I*Sqrt[11] + 7*Sqrt[33]) + (104 - 24*Sqrt[33] + (-13 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + 4*I*(I + Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3))*x)/((-39 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 9*Sqrt[33] + 4*I*(3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))*(1 + x))]) + ((4*2^(2/3) + 2*(-13 + 3*Sqrt[33])^(1/3) - 2^(1/3)*(-13 + 3*Sqrt[33])^(2/3))*(4*2^(2/3)*(I + Sqrt[3]) - 4*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(-I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3))*(4*2^(2/3)*(-I + Sqrt[3]) + 4*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3))*Sqrt[(-39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 9*Sqrt[33] - 4*I*(-3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))/(104 - 24*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3))]*Sqrt[1 + x]*Sqrt[(104 - 24*Sqrt[33] + 2*(1 + 14*I*Sqrt[3] - 6*I*Sqrt[11] + Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-7 - I*Sqrt[3] - 3*I*Sqrt[11] + Sqrt[33])*(-26 + 6*Sqrt[33])^(2/3) + 2*(-52 + 12*Sqrt[33] + 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) - 4*(-26 + 6*Sqrt[33])^(2/3))*x)/((-39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 9*Sqrt[33] - 4*I*(-3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))*(1 + x))]*Sqrt[(104 - 24*Sqrt[33] + 2*(1 - 14*I*Sqrt[3] + 6*I*Sqrt[11] + Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-7 + I*Sqrt[3] + 3*I*Sqrt[11] + Sqrt[33])*(-26 + 6*Sqrt[33])^(2/3) + 2*(-52 + 12*Sqrt[33] + 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) - 4*(-26 + 6*Sqrt[33])^(2/3))*x)/((-39 - 13*I*Sqrt[3] + 9*I*Sqrt[11] + 9*Sqrt[33] + 4*I*(3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))*(1 + x))]*Sqrt[1 + 4*x + 2*x^2 + x^4]*EllipticPi[(2^(1/3)*(4*2^(1/3)*(-3*I + Sqrt[3]) + (3*I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3)))/(4*2^(2/3)*(-I + Sqrt[3]) - 8*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3)), ArcSin[Sqrt[13 - 3*Sqrt[33] - 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) + 4*(-26 + 6*Sqrt[33])^(2/3) + (-39 + 9*Sqrt[33])*x]/(2^(1/6)*Sqrt[3]*(-13 + 3*Sqrt[33])^(2/3)*Sqrt[(-39 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 9*Sqrt[33] - 4*I*(-3*I + Sqrt[3])*(-26 + 6*Sqrt[33])^(1/3))/(104 - 24*Sqrt[33] + (-13 + 13*I*Sqrt[3] - 9*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3) + (-4 - 4*I*Sqrt[3])*(-26 + 6*Sqrt[33])^(2/3))]*Sqrt[1 + x])], (4*(21 - 7*I*Sqrt[3] + 3*I*Sqrt[11] - 3*Sqrt[33]) + (3 + I*Sqrt[3] + 3*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3))/(4*(21 + 7*I*Sqrt[3] - 3*I*Sqrt[11] - 3*Sqrt[33]) + (3 - I*Sqrt[3] - 3*I*Sqrt[11] + 3*Sqrt[33])*(-26 + 6*Sqrt[33])^(1/3))])/(2^(1/6)*Sqrt[3]*(4*2^(2/3)*(I + Sqrt[3]) + 2*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(-I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3) - 6*I*(-13 + 3*Sqrt[33])^(1/3)*x)*(4*2^(2/3)*(-I + Sqrt[3]) - 2*I*(-13 + 3*Sqrt[33])^(1/3) + 2^(1/3)*(I + Sqrt[3])*(-13 + 3*Sqrt[33])^(2/3) + 6*I*(-13 + 3*Sqrt[33])^(1/3)*x)*Sqrt[13 - 3*Sqrt[33] - 2^(1/3)*(-13 + 3*Sqrt[33])^(4/3) + 4*(-26 + 6*Sqrt[33])^(2/3) + (-39 + 9*Sqrt[33])*x]))}
433433

434434

435435
(* It is interesting to see how much of this one can be done; *)

‎0 Independent test suites/Stewart Problems.m

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -262,14 +262,14 @@
262262
{x^4/(-1 + x^4), x, 4, x - ArcTan[x]/2 - ArcTanh[x]/2}
263263

264264
{(-4 + 6*x - x^2 + 3*x^3)/((1 + x^2)*(2 + x^2)), x, 6, -3*ArcTan[x] + Sqrt[2]*ArcTan[x/Sqrt[2]] + (3*Log[1 + x^2])/2}
265-
{(1 + x - 2*x^2 + x^3)/(4 + 5*x^2 + x^4), x, 6, (-3*ArcTan[x/2])/2 + ArcTan[x] + Log[4 + x^2]/2}
265+
{(1 + x - 2*x^2 + x^3)/(4 + 5*x^2 + x^4), x, 7, (-3*ArcTan[x/2])/2 + ArcTan[x] + Log[4 + x^2]/2}
266266
{(-3 + x)/(4 + 2*x + x^2)^2, x, 3, -(7 + 4*x)/(6*(4 + 2*x + x^2)) - (2*ArcTan[(1 + x)/Sqrt[3]])/(3*Sqrt[3])}
267267
{(1 + x^4)/(x*(1 + x^2)^2), x, 3, (1 + x^2)^(-1) + Log[x]}
268268
{(Cos[x]*(-3 + 2*Sin[x]))/(2 - 3*Sin[x] + Sin[x]^2), x, 2, Log[2 - 3*Sin[x] + Sin[x]^2]}
269269
{(Cos[x]^2*Sin[x])/(5 + Cos[x]^2), x, 3, Sqrt[5]*ArcTan[Cos[x]/Sqrt[5]] - Cos[x]}
270270

271271
{1/(x^2 + 2*x - 3), x, 3, Log[1 - x]/4 - Log[3 + x]/4}
272-
{1/(x^2 - 2*x), x, 4, Log[2 - x]/2 - Log[x]/2}
272+
{1/(x^2 - 2*x), x, 1, Log[2 - x]/2 - Log[x]/2}
273273
{(2*x + 1)/(4*x^2 + 12*x - 7), x, 3, Log[1 - 2*x]/8 + (3*Log[7 + 2*x])/8}
274274
{x/(x^2 + x - 1), x, 3, ((5 - Sqrt[5])*Log[1 - Sqrt[5] + 2*x])/10 + ((5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*x])/10}
275275

@@ -301,7 +301,7 @@
301301
{1/(x^(-1/4) + Sqrt[x]), x, 9, 2*Sqrt[x] + (4*ArcTan[(1 - 2*x^(1/4))/Sqrt[3]])/Sqrt[3] + (4*Log[1 + x^(1/4)])/3 - (2*Log[1 - x^(1/4) + Sqrt[x]])/3}
302302
{1/(x^(-1/3) + x^(-1/4)), x, 4, 12*x^(1/12) - 6*x^(1/6) + 4*x^(1/4) - 3*x^(1/3) + (12*x^(5/12))/5 - 2*Sqrt[x] + (12*x^(7/12))/7 - (3*x^(2/3))/2 + (4*x^(3/4))/3 - (6*x^(5/6))/5 + (12*x^(11/12))/11 - x + (12*x^(13/12))/13 - (6*x^(7/6))/7 + (4*x^(5/4))/5 - 12*Log[1 + x^(1/12)]}
303303
{Sqrt[(1 - x)/x], x, 5, Sqrt[-1 + x^(-1)]*x - ArcTan[Sqrt[-1 + x^(-1)]]}
304-
{Cos[x]/(Sin[x] + Sin[x]^2), x, 5, Log[Sin[x]] - Log[1 + Sin[x]]}
304+
{Cos[x]/(Sin[x] + Sin[x]^2), x, 2, Log[Sin[x]] - Log[1 + Sin[x]]}
305305
{E^(2*x)/(2 + 3*E^x + E^(2*x)), x, 4, -Log[1 + E^x] + 2*Log[2 + E^x]}
306306
{1/Sqrt[1 + E^x], x, 3, -2*ArcTanh[Sqrt[1 + E^x]]}
307307
{Sqrt[1 - E^x], x, 4, 2*Sqrt[1 - E^x] - 2*ArcTanh[Sqrt[1 - E^x]]}
@@ -447,7 +447,7 @@
447447
{x^4/E^x, x, 5, -24/E^x - (24*x)/E^x - (12*x^2)/E^x - (4*x^3)/E^x - x^4/E^x}
448448
{x^4/Sqrt[-2 + x^10], x, 3, ArcTanh[x^5/Sqrt[-2 + x^10]]/5}
449449
{E^x*Cos[4 + 3*x], x, 1, (E^x*Cos[4 + 3*x])/10 + (3*E^x*Sin[4 + 3*x])/10}
450-
{E^x*Log[1 + E^x], x, 3, -E^x + (1 + E^x)*Log[1 + E^x]}
450+
{E^x*Log[1 + E^x], x, 4, -E^x + (1 + E^x)*Log[1 + E^x], -E^x + Log[1 + E^x] + E^x*Log[1 + E^x]}
451451
{x^2*ArcTan[x], x, 4, -x^2/6 + (x^3*ArcTan[x])/3 + Log[1 + x^2]/6}
452452
{Sqrt[-1 + E^(2*x)], x, 4, Sqrt[-1 + E^(2*x)] - ArcTan[Sqrt[-1 + E^(2*x)]]}
453453
{E^Sin[x]*Sin[2*x], x, 4, -2*E^Sin[x] + 2*E^Sin[x]*Sin[x]}

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