3.2134 \(\int \frac {1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=166 \[ -\frac {15987390}{456533 \sqrt {1-2 x}}+\frac {1176400}{5929 \sqrt {1-2 x} (5 x+3)}-\frac {35825}{1078 \sqrt {1-2 x} (5 x+3)^2}+\frac {435}{98 \sqrt {1-2 x} (3 x+2) (5 x+3)^2}+\frac {3}{14 \sqrt {1-2 x} (3 x+2)^2 (5 x+3)^2}+\frac {414315}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1561125 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331} \]

[Out]

414315/2401*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))*21^(1/2)-1561125/14641*arctanh(1/11*55^(1/2)*(1-2*x)^(1/2))*55
^(1/2)-15987390/456533/(1-2*x)^(1/2)-35825/1078/(3+5*x)^2/(1-2*x)^(1/2)+3/14/(2+3*x)^2/(3+5*x)^2/(1-2*x)^(1/2)
+435/98/(2+3*x)/(3+5*x)^2/(1-2*x)^(1/2)+1176400/5929/(3+5*x)/(1-2*x)^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 0.07, antiderivative size = 166, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 6, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {103, 151, 152, 156, 63, 206} \[ -\frac {15987390}{456533 \sqrt {1-2 x}}+\frac {1176400}{5929 \sqrt {1-2 x} (5 x+3)}-\frac {35825}{1078 \sqrt {1-2 x} (5 x+3)^2}+\frac {435}{98 \sqrt {1-2 x} (3 x+2) (5 x+3)^2}+\frac {3}{14 \sqrt {1-2 x} (3 x+2)^2 (5 x+3)^2}+\frac {414315}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1561125 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331} \]

Antiderivative was successfully verified.

[In]

Int[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]

[Out]

-15987390/(456533*Sqrt[1 - 2*x]) - 35825/(1078*Sqrt[1 - 2*x]*(3 + 5*x)^2) + 3/(14*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3
+ 5*x)^2) + 435/(98*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^2) + 1176400/(5929*Sqrt[1 - 2*x]*(3 + 5*x)) + (414315*S
qrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1561125*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 103

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*(a +
b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*f)), x] + Dist[1/((m + 1)*(b*
c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*(m + 1) - b*(d*e*(m + n + 2) +
c*f*(m + p + 2)) - b*d*f*(m + n + p + 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && LtQ[m, -1] &&
IntegerQ[m] && (IntegerQ[n] || IntegersQ[2*n, 2*p])

Rule 151

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegerQ[m]

Rule 152

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegersQ[2*m, 2*n, 2*p]

Rule 156

Int[(((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)))/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :>
Dist[(b*g - a*h)/(b*c - a*d), Int[(e + f*x)^p/(a + b*x), x], x] - Dist[(d*g - c*h)/(b*c - a*d), Int[(e + f*x)
^p/(c + d*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin {align*} \int \frac {1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3} \, dx &=\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {1}{14} \int \frac {55-135 x}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3} \, dx\\ &=\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1}{98} \int \frac {5195-15225 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^3} \, dx\\ &=-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}-\frac {\int \frac {296270-1074750 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^2} \, dx}{2156}\\ &=-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1176400}{5929 \sqrt {1-2 x} (3+5 x)}+\frac {\int \frac {5187810-42350400 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx}{23716}\\ &=-\frac {15987390}{456533 \sqrt {1-2 x}}-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1176400}{5929 \sqrt {1-2 x} (3+5 x)}-\frac {\int \frac {-391579365+239810850 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{913066}\\ &=-\frac {15987390}{456533 \sqrt {1-2 x}}-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1176400}{5929 \sqrt {1-2 x} (3+5 x)}-\frac {1242945}{686} \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx+\frac {7805625 \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx}{2662}\\ &=-\frac {15987390}{456533 \sqrt {1-2 x}}-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1176400}{5929 \sqrt {1-2 x} (3+5 x)}+\frac {1242945}{686} \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )-\frac {7805625 \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )}{2662}\\ &=-\frac {15987390}{456533 \sqrt {1-2 x}}-\frac {35825}{1078 \sqrt {1-2 x} (3+5 x)^2}+\frac {3}{14 \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2}+\frac {435}{98 \sqrt {1-2 x} (2+3 x) (3+5 x)^2}+\frac {1176400}{5929 \sqrt {1-2 x} (3+5 x)}+\frac {414315}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1561125 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331}\\ \end {align*}

________________________________________________________________________________________

Mathematica [C]  time = 0.10, size = 83, normalized size = 0.50 \[ \frac {-1102906530 \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {3}{7}-\frac {6 x}{7}\right )[phone] \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};-\frac {5}{11} (2 x-1)\right )+\frac {77 \left (105876000 x^3+201146925 x^2+127185805 x+26765111\right )}{(3 x+2)^2 (5 x+3)^2}}{913066 \sqrt {1-2 x}} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]

[Out]

((77*(26765111 + 127185805*x + 201146925*x^2 + 105876000*x^3))/((2 + 3*x)^2*(3 + 5*x)^2) - 1102906530*Hypergeo
metric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 1070931750*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(9130
66*Sqrt[1 - 2*x])

________________________________________________________________________________________

fricas [A]  time = 0.83, size = 182, normalized size = 1.10 \[ \frac {3748261125 \, \sqrt {11} \sqrt {5} {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 6065985915 \, \sqrt {7} \sqrt {3} {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (-\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \, {\left (7194325500 \, x^{4} + 10073172600 \, x^{3} + 1810042755 \, x^{2} - 2503057145 \, x - 909821467\right )} \sqrt {-2 \, x + 1}}{70306082 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm="fricas")

[Out]

1/70306082*(3748261125*sqrt(11)*sqrt(5)*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log((sqrt(11)*sqrt
(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 6065985915*sqrt(7)*sqrt(3)*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 -
156*x - 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(7194325500*x^4 + 10073172600*x^3
+ 1810042755*x^2 - 2503057145*x - 909821467)*sqrt(-2*x + 1))/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 3
6)

________________________________________________________________________________________

giac [A]  time = 1.31, size = 157, normalized size = 0.95 \[ \frac {1561125}{29282} \, \sqrt {55} \log \left (\frac {{\left | -2 \, \sqrt {55} + 10 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {414315}{4802} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) + \frac {64}{456533 \, \sqrt {-2 \, x + 1}} + \frac {2 \, {\left (256941225 \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + 1747282440 \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - 3958787399 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 2988341532 \, \sqrt {-2 \, x + 1}\right )}}{65219 \, {\left (15 \, {\left (2 \, x - 1\right )}^{2} + 136 \, x + 9\right )}^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm="giac")

[Out]

1561125/29282*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 414315/48
02*sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 64/456533/sqrt(-2*x +
1) + 2/65219*(256941225*(2*x - 1)^3*sqrt(-2*x + 1) + 1747282440*(2*x - 1)^2*sqrt(-2*x + 1) - 3958787399*(-2*x
+ 1)^(3/2) + 2988341532*sqrt(-2*x + 1))/(15*(2*x - 1)^2 + 136*x + 9)^2

________________________________________________________________________________________

maple [A]  time = 0.02, size = 103, normalized size = 0.62 \[ \frac {414315 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{2401}-\frac {1561125 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{14641}+\frac {64}{456533 \sqrt {-2 x +1}}+\frac {-\frac {596875 \left (-2 x +1\right )^{\frac {3}{2}}}{1331}+\frac {118125 \sqrt {-2 x +1}}{121}}{\left (-10 x -6\right )^{2}}-\frac {8748 \left (\frac {217 \left (-2 x +1\right )^{\frac {3}{2}}}{36}-\frac {511 \sqrt {-2 x +1}}{36}\right )}{343 \left (-6 x -4\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(-2*x+1)^(3/2)/(3*x+2)^3/(5*x+3)^3,x)

[Out]

64/456533/(-2*x+1)^(1/2)+312500/1331*(-191/100*(-2*x+1)^(3/2)+2079/500*(-2*x+1)^(1/2))/(-10*x-6)^2-1561125/146
41*arctanh(1/11*55^(1/2)*(-2*x+1)^(1/2))*55^(1/2)-8748/343*(217/36*(-2*x+1)^(3/2)-511/36*(-2*x+1)^(1/2))/(-6*x
-4)^2+414315/2401*arctanh(1/7*21^(1/2)*(-2*x+1)^(1/2))*21^(1/2)

________________________________________________________________________________________

maxima [A]  time = 1.15, size = 155, normalized size = 0.93 \[ \frac {1561125}{29282} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) - \frac {414315}{4802} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) - \frac {2 \, {\left (1798581375 \, {\left (2 \, x - 1\right )}^{4} + 12230911800 \, {\left (2 \, x - 1\right )}^{3} + 27711289905 \, {\left (2 \, x - 1\right )}^{2} + 41836111240 \, x - 20918245348\right )}}{456533 \, {\left (225 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 2040 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 6934 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 10472 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 5929 \, \sqrt {-2 \, x + 1}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm="maxima")

[Out]

1561125/29282*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 414315/4802*sqrt(21
)*log(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) - 2/456533*(1798581375*(2*x - 1)^4 + 12230
911800*(2*x - 1)^3 + 27711289905*(2*x - 1)^2 + 41836111240*x - 20918245348)/(225*(-2*x + 1)^(9/2) - 2040*(-2*x
+ 1)^(7/2) + 6934*(-2*x + 1)^(5/2) - 10472*(-2*x + 1)^(3/2) + 5929*sqrt(-2*x + 1))

________________________________________________________________________________________

mupad [B]  time = 1.28, size = 117, normalized size = 0.70 \[ \frac {414315\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{2401}-\frac {1561125\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{14641}-\frac {\frac {217330448\,x}{266805}+\frac {3694838654\,{\left (2\,x-1\right )}^2}{6847995}+\frac {108719216\,{\left (2\,x-1\right )}^3}{456533}+\frac {15987390\,{\left (2\,x-1\right )}^4}{456533}-\frac {543331048}{1334025}}{\frac {5929\,\sqrt {1-2\,x}}{225}-\frac {10472\,{\left (1-2\,x\right )}^{3/2}}{225}+\frac {6934\,{\left (1-2\,x\right )}^{5/2}}{225}-\frac {136\,{\left (1-2\,x\right )}^{7/2}}{15}+{\left (1-2\,x\right )}^{9/2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((1 - 2*x)^(3/2)*(3*x + 2)^3*(5*x + 3)^3),x)

[Out]

(414315*21^(1/2)*atanh((21^(1/2)*(1 - 2*x)^(1/2))/7))/2401 - (1561125*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2)
)/11))/14641 - ((217330448*x)/266805 + (3694838654*(2*x - 1)^2)/6847995 + (108719216*(2*x - 1)^3)/456533 + (15
987390*(2*x - 1)^4)/456533 - 543331048/1334025)/((5929*(1 - 2*x)^(1/2))/225 - (10472*(1 - 2*x)^(3/2))/225 + (6
934*(1 - 2*x)^(5/2))/225 - (136*(1 - 2*x)^(7/2))/15 + (1 - 2*x)^(9/2))

________________________________________________________________________________________

sympy [C]  time = 28.06, size = 5828, normalized size = 35.11 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)**(3/2)/(2+3*x)**3/(3+5*x)**3,x)

[Out]

97154928360000000*sqrt(55)*(x - 1/2)**(21/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(2
1/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x -
1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 5396305527360
3168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 157230
354916800000*sqrt(21)*(x - 1/2)**(21/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) +
8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**
(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*
(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 4857746418000
0000*sqrt(55)*pi*(x - 1/2)**(21/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2)
+ 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1
/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064
*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 78615177458400000*sqrt(21)*pi*(x - 1/2)**(21/2)/(
911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(1
7/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x
- 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 24714725830953
62*I*(x - 1/2)**(5/2)) + 880871350464000000*sqrt(55)*(x - 1/2)**(19/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(91116
6822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2)
+ 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/
2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*
(x - 1/2)**(5/2)) - 1425555217912320000*sqrt(21)*(x - 1/2)**(19/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(91116682272
0000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 7425
0241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(1
1/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1
/2)**(5/2)) - 440435675232000000*sqrt(55)*pi*(x - 1/2)**(19/2)/(911166822720000*I*(x - 1/2)**(21/2) + 82612458
59328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) +
105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2
)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 712777608956160000*sq
rt(21)*pi*(x - 1/2)**(19/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 3276
5558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(1
3/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x -
1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 3493691223825600000*sqrt(55)*(x - 1/2)**(17/2)*atan(sqrt
(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558
945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2)
+ 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2
)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 5654003562808128000*sqrt(21)*(x - 1/2)**(17/2)*atan(sqrt(42)
*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011
200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 952
87810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/
2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 1746845611912800000*sqrt(55)*pi*(x - 1/2)**(17/2)/(911166822720000
*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241
951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2)
+ 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)*
*(5/2)) + 2827001781404064000*sqrt(21)*pi*(x - 1/2)**(17/2)/(911166822720000*I*(x - 1/2)**(21/2) + 82612458593
28000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 10
5148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**
(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 7917075948781440000*sqrt
(55)*(x - 1/2)**(15/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(21/2) + 826124585932800
0*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148
838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2
) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 12812573508547507200*sqrt(21
)*(x - 1/2)**(15/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(
x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 10514883807
4841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1
7460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 3958537974390720000*sqrt(55)*pi*(
x - 1/2)**(15/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 327655589450112
00*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 9528
7810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2
) + 2471472583095362*I*(x - 1/2)**(5/2)) + 6406286754273753600*sqrt(21)*pi*(x - 1/2)**(15/2)/(911166822720000*
I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 742502419
51226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2)
+ 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**
(5/2)) + 11211698643507096000*sqrt(55)*(x - 1/2)**(13/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(
x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 742502419512
26880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 5
3963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/
2)) - 18144415179915900480*sqrt(21)*(x - 1/2)**(13/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1
/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880
*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 539630
55273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) -
5605849321753548000*sqrt(55)*pi*(x - 1/2)**(13/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(
x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 10514883807
4841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1
7460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 9072207589957950240*sqrt(21)*pi*(
x - 1/2)**(13/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 327655589450112
00*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 9528
7810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2
) + 2471472583095362*I*(x - 1/2)**(5/2)) + 10160247467602848000*sqrt(55)*(x - 1/2)**(11/2)*atan(sqrt(110)*sqrt
(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*
I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 9528781
0504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) +
2471472583095362*I*(x - 1/2)**(5/2)) - 16442802669302634240*sqrt(21)*(x - 1/2)**(11/2)*atan(sqrt(42)*sqrt(x -
1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x
- 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 952878105040
74496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471
472583095362*I*(x - 1/2)**(5/2)) - 5080123733801424000*sqrt(55)*pi*(x - 1/2)**(11/2)/(911166822720000*I*(x - 1
/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880
*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 539630
55273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) +
8221401334651317120*sqrt(21)*pi*(x - 1/2)**(11/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(
x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 10514883807
4841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1
7460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 5753915351683884000*sqrt(55)*(x -
1/2)**(9/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1
/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 1051488380748417
92*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 174607
93314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 9311829756635941920*sqrt(21)*(x - 1/2)
**(9/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(1
9/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x
- 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1746079331433
6064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 2876957675841942000*sqrt(55)*pi*(x - 1/2)**(9
/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2
)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496
*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 247147258
3095362*I*(x - 1/2)**(5/2)) + 4655914878317970960*sqrt(21)*pi*(x - 1/2)**(9/2)/(911166822720000*I*(x - 1/2)**(
21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x
- 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 539630552736
03168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 18617
90927043432000*sqrt(55)*(x - 1/2)**(7/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822720000*I*(x - 1/2)**(21/2)
+ 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2
)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168
*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 3013023149
533172160*sqrt(21)*(x - 1/2)**(7/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I*(x - 1/2)**(21/2) + 8261
245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/
2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x -
1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 93089546352171600
0*sqrt(55)*pi*(x - 1/2)**(7/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 3
2765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)*
*(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(
x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 1506511574766586080*sqrt(21)*pi*(x - 1/2)**(7/2)/(911
166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2
) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x -
1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*
I*(x - 1/2)**(5/2)) + 263525554011662250*sqrt(55)*(x - 1/2)**(5/2)*atan(sqrt(110)*sqrt(x - 1/2)/11)/(911166822
720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74
250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**
(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x -
1/2)**(5/2)) - 426475703150835030*sqrt(21)*(x - 1/2)**(5/2)*atan(sqrt(42)*sqrt(x - 1/2)/7)/(911166822720000*I
*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 7425024195
1226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) +
53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(
5/2)) - 131762777005831125*sqrt(55)*pi*(x - 1/2)**(5/2)/(911166822720000*I*(x - 1/2)**(21/2) + 826124585932800
0*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148
838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2
) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) + 213237851575417515*sqrt(21)*
pi*(x - 1/2)**(5/2)/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 327655589450
11200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 9
5287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(
7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 15954136228800000*sqrt(2)*(x - 1/2)**10/(911166822720000*I*(x -
1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 7425024195122688
0*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963
055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2))
- 126571957585920000*sqrt(2)*(x - 1/2)**9/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)*
*(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I
*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1746079331
4336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 430287960796848000*sqrt(2)*(x - 1/2)**8/(9
11166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17
/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x
- 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 247147258309536
2*I*(x - 1/2)**(5/2)) - 812535935908435200*sqrt(2)*(x - 1/2)**7/(911166822720000*I*(x - 1/2)**(21/2) + 8261245
859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2)
+ 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/
2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 920473454994619680*s
qrt(2)*(x - 1/2)**6/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 327655589450
11200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 9
5287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(
7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 625554301151866240*sqrt(2)*(x - 1/2)**5/(911166822720000*I*(x -
1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 7425024195122688
0*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963
055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2))
- 236145325246866728*sqrt(2)*(x - 1/2)**4/(911166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)*
*(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I
*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 1746079331
4336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2)) - 38198518801324112*sqrt(2)*(x - 1/2)**3/(91
1166822720000*I*(x - 1/2)**(21/2) + 8261245859328000*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/
2) + 74250241951226880*I*(x - 1/2)**(15/2) + 105148838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x -
1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362
*I*(x - 1/2)**(5/2)) + 173234186048*sqrt(2)*(x - 1/2)**2/(911166822720000*I*(x - 1/2)**(21/2) + 82612458593280
00*I*(x - 1/2)**(19/2) + 32765558945011200*I*(x - 1/2)**(17/2) + 74250241951226880*I*(x - 1/2)**(15/2) + 10514
8838074841792*I*(x - 1/2)**(13/2) + 95287810504074496*I*(x - 1/2)**(11/2) + 53963055273603168*I*(x - 1/2)**(9/
2) + 17460793314336064*I*(x - 1/2)**(7/2) + 2471472583095362*I*(x - 1/2)**(5/2))

________________________________________________________________________________________