Integrand size = 25, antiderivative size = 554 \[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=-\frac {2 \sqrt {\frac {2}{3}} \left (2 \left (767+532 \sqrt {6}\right )-\frac {5 \left (10636-2629 \sqrt {6}\right ) \sqrt {-2+8 x-5 x^2}}{\left (13-2 \sqrt {6}\right ) \left (4-\sqrt {6}-5 x\right )}\right )}{3105 \left (13+2 \sqrt {6}-\frac {10 \sqrt {6} \sqrt {-2+8 x-5 x^2}}{4-\sqrt {6}-5 x}-\frac {5 \left (13-2 \sqrt {6}\right ) \left (2-8 x+5 x^2\right )}{\left (4-\sqrt {6}-5 x\right )^2}\right )}+\frac {8 \left (2+\frac {5 \sqrt {-2+8 x-5 x^2}}{4-\sqrt {6}-5 x}\right )}{15 \left (1-\frac {5 \left (2-8 x+5 x^2\right )}{\left (4-\sqrt {6}-5 x\right )^2}\right ) \left (13+2 \sqrt {6}-\frac {10 \sqrt {6} \sqrt {-2+8 x-5 x^2}}{4-\sqrt {6}-5 x}-\frac {5 \left (13-2 \sqrt {6}\right ) \left (2-8 x+5 x^2\right )}{\left (4-\sqrt {6}-5 x\right )^2}\right )}+\frac {212 \arctan \left (\frac {\sqrt {5} \sqrt {-2+8 x-5 x^2}}{4-\sqrt {6}-5 x}\right )}{729 \sqrt {5}}+\frac {14600 \arctan \left (\frac {6+\frac {\left (12-13 \sqrt {6}\right ) \sqrt {-2+8 x-5 x^2}}{4-\sqrt {6}-5 x}}{\sqrt {138}}\right )}{16767 \sqrt {23}}-\frac {100}{729} \log \left (\frac {2 \left (3-2 \sqrt {6}\right )+5 \sqrt {6} x}{\left (4-\sqrt {6}-5 x\right )^2}\right )+\frac {100}{729} \log \left (\frac {2 \left (3-2 \sqrt {6}\right )+12 x-3 \sqrt {6} x+10 \sqrt {6} x^2+6 \sqrt {-2+8 x-5 x^2}-4 \sqrt {6} \sqrt {-2+8 x-5 x^2}+5 \sqrt {6} x \sqrt {-2+8 x-5 x^2}}{\left (4-\sqrt {6}-5 x\right )^2}\right ) \] Output:
-2/3*6^(1/2)*(1534+1064*6^(1/2)-5*(10636-2629*6^(1/2))*(-5*x^2+8*x-2)^(1/2 )/(13-2*6^(1/2))/(4-6^(1/2)-5*x))/(40365+6210*6^(1/2)-31050*6^(1/2)*(-5*x^ 2+8*x-2)^(1/2)/(4-6^(1/2)-5*x)-15525*(13-2*6^(1/2))*(5*x^2-8*x+2)/(4-6^(1/ 2)-5*x)^2)+8/15*(2+5*(-5*x^2+8*x-2)^(1/2)/(4-6^(1/2)-5*x))/(1-5*(5*x^2-8*x +2)/(4-6^(1/2)-5*x)^2)/(13+2*6^(1/2)-10*6^(1/2)*(-5*x^2+8*x-2)^(1/2)/(4-6^ (1/2)-5*x)-5*(13-2*6^(1/2))*(5*x^2-8*x+2)/(4-6^(1/2)-5*x)^2)+212/3645*arct an(5^(1/2)*(-5*x^2+8*x-2)^(1/2)/(4-6^(1/2)-5*x))*5^(1/2)+14600/385641*arct an(1/138*(6+(12-13*6^(1/2))*(-5*x^2+8*x-2)^(1/2)/(4-6^(1/2)-5*x))*138^(1/2 ))*23^(1/2)-100/729*ln((6-4*6^(1/2)+5*x*6^(1/2))/(4-6^(1/2)-5*x)^2)+100/72 9*ln((6-4*6^(1/2)+12*x-3*x*6^(1/2)+10*6^(1/2)*x^2+6*(-5*x^2+8*x-2)^(1/2)-4 *6^(1/2)*(-5*x^2+8*x-2)^(1/2)+5*6^(1/2)*x*(-5*x^2+8*x-2)^(1/2))/(4-6^(1/2) -5*x)^2)
Result contains complex when optimal does not.
Time = 8.22 (sec) , antiderivative size = 1128, normalized size of antiderivative = 2.04 \[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx =\text {Too large to display} \] Input:
Integrate[x^2/(1 + 2*x + Sqrt[-2 + 8*x - 5*x^2])^2,x]
Output:
(-23805*x + (115*(3126 - 6247*x))/(3 - 4*x + 9*x^2) - (1035*Sqrt[-2 + 8*x - 5*x^2]*(336 - 799*x + 828*x^2))/(3 - 4*x + 9*x^2) - 56074*Sqrt[5]*ArcSin [(4 - 5*x)/Sqrt[6]] + 36500*Sqrt[23]*ArcTan[(-2 + 9*x)/Sqrt[23]] - ((250*I )*(-109*I + 445*Sqrt[23])*ArcTan[(23*(-625034999 + (31717972*I)*Sqrt[23] + 8*(65984878 - (56521751*I)*Sqrt[23])*x + (85877608 + (2214584710*I)*Sqrt[ 23])*x^2 + 900*(7286713 - (4610645*I)*Sqrt[23])*x^3 + (10125*I)*(791161*I + 205946*Sqrt[23])*x^4))/(9763896428*I + 2370058321*Sqrt[23] - 2025*(-5801 198*I + 12282473*Sqrt[23])*x^4 - 246588624*Sqrt[23*(77 - (52*I)*Sqrt[23])] *Sqrt[-2 + 8*x - 5*x^2] + 36*x^3*(-4062801535*I + 1309323961*Sqrt[23] + 25 686315*Sqrt[23*(77 - (52*I)*Sqrt[23])]*Sqrt[-2 + 8*x - 5*x^2]) - 2*x^2*(-1 16526334717*I + 8516310250*Sqrt[23] + 575373456*Sqrt[23*(77 - (52*I)*Sqrt[ 23])]*Sqrt[-2 + 8*x - 5*x^2]) + x*(-90041575208*I - 6413927920*Sqrt[23] + 637020612*Sqrt[23*(77 - (52*I)*Sqrt[23])]*Sqrt[-2 + 8*x - 5*x^2]))])/Sqrt[ 77/23 - (52*I)/Sqrt[23]] + (250*(109 - (445*I)*Sqrt[23])*ArcTan[(23*(-6250 34999 - (31717972*I)*Sqrt[23] + 8*(65984878 + (56521751*I)*Sqrt[23])*x + ( 85877608 - (2214584710*I)*Sqrt[23])*x^2 + 900*(7286713 + (4610645*I)*Sqrt[ 23])*x^3 - (10125*I)*(-791161*I + 205946*Sqrt[23])*x^4))/(9763896428*I - 2 370058321*Sqrt[23] + 2025*(5801198*I + 12282473*Sqrt[23])*x^4 + 246588624* Sqrt[23*(77 + (52*I)*Sqrt[23])]*Sqrt[-2 + 8*x - 5*x^2] + x*(-90041575208*I + 6413927920*Sqrt[23] - 637020612*Sqrt[23*(77 + (52*I)*Sqrt[23])]*Sqrt...
Time = 0.84 (sec) , antiderivative size = 253, normalized size of antiderivative = 0.46, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x^2}{\left (\sqrt {-5 x^2+8 x-2}+2 x+1\right )^2} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {4 \sqrt {-5 x^2+8 x-2} x}{9 \left (9 x^2-4 x+3\right )}-\frac {28 \sqrt {-5 x^2+8 x-2} x}{81 \left (9 x^2-4 x+3\right )^2}+\frac {900 x+389}{729 \left (9 x^2-4 x+3\right )}-\frac {34 \sqrt {-5 x^2+8 x-2}}{81 \left (9 x^2-4 x+3\right )}-\frac {2 (680 x+543)}{729 \left (9 x^2-4 x+3\right )^2}+\frac {34 \sqrt {-5 x^2+8 x-2}}{27 \left (9 x^2-4 x+3\right )^2}-\frac {1}{81}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {34}{729} \sqrt {5} \arcsin \left (\frac {4-5 x}{\sqrt {6}}\right )+\frac {64 \arcsin \left (\frac {4-5 x}{\sqrt {6}}\right )}{729 \sqrt {5}}+\frac {7300 \arctan \left (\frac {8-13 x}{\sqrt {23} \sqrt {-5 x^2+8 x-2}}\right )}{16767 \sqrt {23}}-\frac {7300 \arctan \left (\frac {2-9 x}{\sqrt {23}}\right )}{16767 \sqrt {23}}+\frac {100}{729} \text {arctanh}\left (\frac {2 x+1}{\sqrt {-5 x^2+8 x-2}}\right )+\frac {3126-6247 x}{16767 \left (9 x^2-4 x+3\right )}-\frac {4}{81} \sqrt {-5 x^2+8 x-2}-\frac {17 (2-9 x) \sqrt {-5 x^2+8 x-2}}{621 \left (9 x^2-4 x+3\right )}+\frac {14 (3-2 x) \sqrt {-5 x^2+8 x-2}}{1863 \left (9 x^2-4 x+3\right )}+\frac {50}{729} \log \left (9 x^2-4 x+3\right )-\frac {x}{81}\) |
Input:
Int[x^2/(1 + 2*x + Sqrt[-2 + 8*x - 5*x^2])^2,x]
Output:
-1/81*x - (4*Sqrt[-2 + 8*x - 5*x^2])/81 + (3126 - 6247*x)/(16767*(3 - 4*x + 9*x^2)) - (17*(2 - 9*x)*Sqrt[-2 + 8*x - 5*x^2])/(621*(3 - 4*x + 9*x^2)) + (14*(3 - 2*x)*Sqrt[-2 + 8*x - 5*x^2])/(1863*(3 - 4*x + 9*x^2)) + (64*Arc Sin[(4 - 5*x)/Sqrt[6]])/(729*Sqrt[5]) - (34*Sqrt[5]*ArcSin[(4 - 5*x)/Sqrt[ 6]])/729 - (7300*ArcTan[(2 - 9*x)/Sqrt[23]])/(16767*Sqrt[23]) + (7300*ArcT an[(8 - 13*x)/(Sqrt[23]*Sqrt[-2 + 8*x - 5*x^2])])/(16767*Sqrt[23]) + (100* ArcTanh[(1 + 2*x)/Sqrt[-2 + 8*x - 5*x^2]])/729 + (50*Log[3 - 4*x + 9*x^2]) /729
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.99 (sec) , antiderivative size = 1172, normalized size of antiderivative = 2.12
| method | result | size |
| trager | \(\text {Expression too large to display}\) | \(1172\) |
| default | \(\text {Expression too large to display}\) | \(6561\) |
Input:
int(x^2/(1+2*x+(-5*x^2+8*x-2)^(1/2))^2,x,method=_RETURNVERBOSE)
Output:
-1/1863*(207*x^2+950*x+300)*x/(9*x^2-4*x+3)-1/1863*(828*x^2-799*x+336)/(9* x^2-4*x+3)*(-5*x^2+8*x-2)^(1/2)+200/729*ln(37671726726*RootOf(135*_Z^2+115 00*_Z+299943)^2*RootOf(621*_Z^2-52900*_Z+1620000)^2*x+2468671220475*RootOf (135*_Z^2+11500*_Z+299943)*RootOf(621*_Z^2-52900*_Z+1620000)^2*x-395650312 1550*RootOf(135*_Z^2+11500*_Z+299943)^2*RootOf(621*_Z^2-52900*_Z+1620000)* x-855439149960*RootOf(135*_Z^2+11500*_Z+299943)*RootOf(621*_Z^2-52900*_Z+1 620000)*(-5*x^2+8*x-2)^(1/2)+40244022639756*RootOf(621*_Z^2-52900*_Z+16200 00)^2*x-239945560251300*RootOf(621*_Z^2-52900*_Z+1620000)*RootOf(135*_Z^2+ 11500*_Z+299943)*x+101037495487500*RootOf(135*_Z^2+11500*_Z+299943)^2*x+27 0740228057280*(-5*x^2+8*x-2)^(1/2)*RootOf(621*_Z^2-52900*_Z+1620000)-24887 1188718000*RootOf(135*_Z^2+11500*_Z+299943)*(-5*x^2+8*x-2)^(1/2)-273243179 64420*RootOf(135*_Z^2+11500*_Z+299943)*RootOf(621*_Z^2-52900*_Z+1620000)-3 601271727150750*RootOf(621*_Z^2-52900*_Z+1620000)*x+5636016844605000*RootO f(135*_Z^2+11500*_Z+299943)*x-19985447861813000*(-5*x^2+8*x-2)^(1/2)-83238 7238465040*RootOf(621*_Z^2-52900*_Z+1620000)+1197372142395000*RootOf(135*_ Z^2+11500*_Z+299943)+78089605249347500*x+30714221756597000)-2/621*ln(37671 726726*RootOf(135*_Z^2+11500*_Z+299943)^2*RootOf(621*_Z^2-52900*_Z+1620000 )^2*x+2468671220475*RootOf(135*_Z^2+11500*_Z+299943)*RootOf(621*_Z^2-52900 *_Z+1620000)^2*x-3956503121550*RootOf(135*_Z^2+11500*_Z+299943)^2*RootOf(6 21*_Z^2-52900*_Z+1620000)*x-855439149960*RootOf(135*_Z^2+11500*_Z+29994...
Time = 0.10 (sec) , antiderivative size = 374, normalized size of antiderivative = 0.68 \[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=-\frac {214245 \, x^{3} - 36500 \, \sqrt {23} {\left (9 \, x^{2} - 4 \, x + 3\right )} \arctan \left (\frac {1}{23} \, \sqrt {23} {\left (9 \, x - 2\right )}\right ) + 56074 \, \sqrt {5} {\left (9 \, x^{2} - 4 \, x + 3\right )} \arctan \left (\frac {\sqrt {5} \sqrt {-5 \, x^{2} + 8 \, x - 2} {\left (5 \, x - 4\right )}}{5 \, {\left (5 \, x^{2} - 8 \, x + 2\right )}}\right ) - 18250 \, \sqrt {23} {\left (9 \, x^{2} - 4 \, x + 3\right )} \arctan \left (\frac {\sqrt {23} \sqrt {-5 \, x^{2} + 8 \, x - 2} {\left (13 \, x - 8\right )} + 2 \, \sqrt {23} {\left (2 \, x^{2} - 3 \, x\right )}}{23 \, {\left (7 \, x^{2} - 8 \, x + 2\right )}}\right ) - 18250 \, \sqrt {23} {\left (9 \, x^{2} - 4 \, x + 3\right )} \arctan \left (\frac {\sqrt {23} \sqrt {-5 \, x^{2} + 8 \, x - 2} {\left (13 \, x - 8\right )} - 2 \, \sqrt {23} {\left (2 \, x^{2} - 3 \, x\right )}}{23 \, {\left (7 \, x^{2} - 8 \, x + 2\right )}}\right ) - 95220 \, x^{2} - 132250 \, {\left (9 \, x^{2} - 4 \, x + 3\right )} \log \left (9 \, x^{2} - 4 \, x + 3\right ) + 66125 \, {\left (9 \, x^{2} - 4 \, x + 3\right )} \log \left (-\frac {x^{2} + 2 \, \sqrt {-5 \, x^{2} + 8 \, x - 2} {\left (2 \, x + 1\right )} - 12 \, x + 1}{x^{2}}\right ) - 66125 \, {\left (9 \, x^{2} - 4 \, x + 3\right )} \log \left (-\frac {x^{2} - 2 \, \sqrt {-5 \, x^{2} + 8 \, x - 2} {\left (2 \, x + 1\right )} - 12 \, x + 1}{x^{2}}\right ) + 1035 \, {\left (828 \, x^{2} - 799 \, x + 336\right )} \sqrt {-5 \, x^{2} + 8 \, x - 2} + 789820 \, x - 359490}{1928205 \, {\left (9 \, x^{2} - 4 \, x + 3\right )}} \] Input:
integrate(x^2/(1+2*x+(-5*x^2+8*x-2)^(1/2))^2,x, algorithm="fricas")
Output:
-1/1928205*(214245*x^3 - 36500*sqrt(23)*(9*x^2 - 4*x + 3)*arctan(1/23*sqrt (23)*(9*x - 2)) + 56074*sqrt(5)*(9*x^2 - 4*x + 3)*arctan(1/5*sqrt(5)*sqrt( -5*x^2 + 8*x - 2)*(5*x - 4)/(5*x^2 - 8*x + 2)) - 18250*sqrt(23)*(9*x^2 - 4 *x + 3)*arctan(1/23*(sqrt(23)*sqrt(-5*x^2 + 8*x - 2)*(13*x - 8) + 2*sqrt(2 3)*(2*x^2 - 3*x))/(7*x^2 - 8*x + 2)) - 18250*sqrt(23)*(9*x^2 - 4*x + 3)*ar ctan(1/23*(sqrt(23)*sqrt(-5*x^2 + 8*x - 2)*(13*x - 8) - 2*sqrt(23)*(2*x^2 - 3*x))/(7*x^2 - 8*x + 2)) - 95220*x^2 - 132250*(9*x^2 - 4*x + 3)*log(9*x^ 2 - 4*x + 3) + 66125*(9*x^2 - 4*x + 3)*log(-(x^2 + 2*sqrt(-5*x^2 + 8*x - 2 )*(2*x + 1) - 12*x + 1)/x^2) - 66125*(9*x^2 - 4*x + 3)*log(-(x^2 - 2*sqrt( -5*x^2 + 8*x - 2)*(2*x + 1) - 12*x + 1)/x^2) + 1035*(828*x^2 - 799*x + 336 )*sqrt(-5*x^2 + 8*x - 2) + 789820*x - 359490)/(9*x^2 - 4*x + 3)
\[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=\int \frac {x^{2}}{\left (2 x + \sqrt {- 5 x^{2} + 8 x - 2} + 1\right )^{2}}\, dx \] Input:
integrate(x**2/(1+2*x+(-5*x**2+8*x-2)**(1/2))**2,x)
Output:
Integral(x**2/(2*x + sqrt(-5*x**2 + 8*x - 2) + 1)**2, x)
\[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=\int { \frac {x^{2}}{{\left (2 \, x + \sqrt {-5 \, x^{2} + 8 \, x - 2} + 1\right )}^{2}} \,d x } \] Input:
integrate(x^2/(1+2*x+(-5*x^2+8*x-2)^(1/2))^2,x, algorithm="maxima")
Output:
integrate(x^2/(2*x + sqrt(-5*x^2 + 8*x - 2) + 1)^2, x)
Time = 0.17 (sec) , antiderivative size = 673, normalized size of antiderivative = 1.21 \[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx =\text {Too large to display} \] Input:
integrate(x^2/(1+2*x+(-5*x^2+8*x-2)^(1/2))^2,x, algorithm="giac")
Output:
106/3645*sqrt(5)*arcsin(1/6*sqrt(6)*(5*x - 4)) + 7300/385641*sqrt(23)*arct an(1/23*sqrt(23)*(9*x - 2)) - 1/81*x + 7300/16767*(5*sqrt(6) + 13*sqrt(5)) *arctan(-(26*sqrt(6) + 12*sqrt(5) - 139*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))/(5*x - 4))/(5*sqrt(138) + 13*sqrt(115)))/(5*sqrt(138) + 13*sqrt(1 15)) + 7300/16767*(5*sqrt(6) - 13*sqrt(5))*arctan((26*sqrt(6) - 12*sqrt(5) - 139*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))/(5*x - 4))/(5*sqrt(138) - 13*sqrt(115)))/(5*sqrt(138) - 13*sqrt(115)) - 4/81*sqrt(-5*x^2 + 8*x - 2 ) - 1/16767*(6247*x - 3126)/(9*x^2 - 4*x + 3) - 4/258957*(98968*sqrt(30) - 42417*sqrt(5)*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^3/(5*x - 4)^3 + 175864*sqrt(30)*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^2/(5*x - 4)^2 - 401871*sqrt(5)*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))/(5*x - 4))/(104 *sqrt(6)*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^3/(5*x - 4)^3 + 104*sq rt(6)*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))/(5*x - 4) - 139*(sqrt(5)* sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^4/(5*x - 4)^4 - 494*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^2/(5*x - 4)^2 - 139) + 50/729*log(9*x^2 - 4*x + 3) + 50/729*log(-4*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))*(13*sqrt(6) + 6 *sqrt(5))/(5*x - 4) + 26*sqrt(30) + 139*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^2/(5*x - 4)^2 + 199) - 50/729*log(-4*(sqrt(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))*(13*sqrt(6) - 6*sqrt(5))/(5*x - 4) - 26*sqrt(30) + 139*(sqr t(5)*sqrt(-5*x^2 + 8*x - 2) - sqrt(6))^2/(5*x - 4)^2 + 199)
Timed out. \[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=\int \frac {x^2}{{\left (2\,x+\sqrt {-5\,x^2+8\,x-2}+1\right )}^2} \,d x \] Input:
int(x^2/(2*x + (8*x - 5*x^2 - 2)^(1/2) + 1)^2,x)
Output:
int(x^2/(2*x + (8*x - 5*x^2 - 2)^(1/2) + 1)^2, x)
\[ \int \frac {x^2}{\left (1+2 x+\sqrt {-2+8 x-5 x^2}\right )^2} \, dx=\text {too large to display} \] Input:
int(x^2/(1+2*x+(-5*x^2+8*x-2)^(1/2))^2,x)
Output:
( - 8828804488369232499186880557033714828296118355174650*sqrt(30)*asin((5* x - 4)/sqrt(6))*x**4 + 282521743627815439973980177825078874505475787365588 80*sqrt(30)*asin((5*x - 4)/sqrt(6))*x**3 - 3302190873822645281424268313035 7212893587555763996444*sqrt(30)*asin((5*x - 4)/sqrt(6))*x**2 + 16672270796 801948186118830246961444693039188439598944*sqrt(30)*asin((5*x - 4)/sqrt(6) )*x - 6422137783391545417927049412597857749175398685023338*sqrt(30)*asin(( 5*x - 4)/sqrt(6)) - 50001612112790173069463242181692249523147778847200000* asin((5*x - 4)/sqrt(6))*x**4 + 1600051587609285538222823749814151984740728 92311040000*asin((5*x - 4)/sqrt(6))*x**3 - 1870183753789001337422788129798 20789080652482463552000*asin((5*x - 4)/sqrt(6))*x**2 + 9442279739225166509 5124660791501808482230669783552000*asin((5*x - 4)/sqrt(6))*x - 36371543033 155518484602150979571695579060088020704000*asin((5*x - 4)/sqrt(6)) - 50230 82427577640658214878110604507356708059200000000*sqrt( - 5*x**2 + 8*x - 2)* sqrt(5)*x**4 + 10574467790714450582797527188537906108630869077360000*sqrt( - 5*x**2 + 8*x - 2)*sqrt(5)*x**3 + 10149621181905563417624564385032288228 48446566336000*sqrt( - 5*x**2 + 8*x - 2)*sqrt(5)*x**2 - 255858000475527431 38647098256304550501840359332950400*sqrt( - 5*x**2 + 8*x - 2)*sqrt(5)*x + 14735309132025224813466775966821188280137059334376960*sqrt( - 5*x**2 + 8*x - 2)*sqrt(5) - 5929350590217801701100698231982505402726664999585500*sqrt( - 5*x**2 + 8*x - 2)*sqrt(6)*x**4 + 13047981220551499091247024490003412...