3.20.75 \(\int \frac {1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=132 \[ -\frac {12790}{3773 \sqrt {1-2 x}}+\frac {565}{49 \sqrt {1-2 x} (3 x+2)}+\frac {8}{7 \sqrt {1-2 x} (3 x+2)^2}+\frac {1}{7 \sqrt {1-2 x} (3 x+2)^3}+\frac {40140}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1250}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \]

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Rubi [A]  time = 0.06, antiderivative size = 132, normalized size of antiderivative = 1.00, number of steps used = 9, 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} \begin {gather*} -\frac {12790}{3773 \sqrt {1-2 x}}+\frac {565}{49 \sqrt {1-2 x} (3 x+2)}+\frac {8}{7 \sqrt {1-2 x} (3 x+2)^2}+\frac {1}{7 \sqrt {1-2 x} (3 x+2)^3}+\frac {40140}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1250}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

-12790/(3773*Sqrt[1 - 2*x]) + 1/(7*Sqrt[1 - 2*x]*(2 + 3*x)^3) + 8/(7*Sqrt[1 - 2*x]*(2 + 3*x)^2) + 565/(49*Sqrt
[1 - 2*x]*(2 + 3*x)) + (40140*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1250*Sqrt[5/11]*ArcTanh[Sqrt[
5/11]*Sqrt[1 - 2*x]])/11

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)^4 (3+5 x)} \, dx &=\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {1}{21} \int \frac {42-105 x}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)} \, dx\\ &=\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {1}{294} \int \frac {2310-8400 x}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)} \, dx\\ &=\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {565}{49 \sqrt {1-2 x} (2+3 x)}+\frac {\int \frac {43680-355950 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx}{2058}\\ &=-\frac {12790}{3773 \sqrt {1-2 x}}+\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {565}{49 \sqrt {1-2 x} (2+3 x)}-\frac {\int \frac {-3293220+2014425 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{79233}\\ &=-\frac {12790}{3773 \sqrt {1-2 x}}+\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {565}{49 \sqrt {1-2 x} (2+3 x)}-\frac {60210}{343} \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx+\frac {3125}{11} \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx\\ &=-\frac {12790}{3773 \sqrt {1-2 x}}+\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {565}{49 \sqrt {1-2 x} (2+3 x)}+\frac {60210}{343} \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )-\frac {3125}{11} \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )\\ &=-\frac {12790}{3773 \sqrt {1-2 x}}+\frac {1}{7 \sqrt {1-2 x} (2+3 x)^3}+\frac {8}{7 \sqrt {1-2 x} (2+3 x)^2}+\frac {565}{49 \sqrt {1-2 x} (2+3 x)}+\frac {40140}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1250}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )\\ \end {align*}

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Mathematica [C]  time = 0.06, size = 85, normalized size = 0.64 \begin {gather*} \frac {-441540 (3 x+2)^3 \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {3}{7}-\frac {6 x}{7}\right )+428750 (3 x+2)^3 \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};-\frac {5}{11} (2 x-1)\right )+231 \left (1695 x^2+2316 x+793\right )}{3773 \sqrt {1-2 x} (3 x+2)^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

(231*(793 + 2316*x + 1695*x^2) - 441540*(2 + 3*x)^3*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 428750*(2
+ 3*x)^3*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(3773*Sqrt[1 - 2*x]*(2 + 3*x)^3)

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IntegrateAlgebraic [A]  time = 0.33, size = 110, normalized size = 0.83 \begin {gather*} -\frac {2 \left (172665 (1-2 x)^3-817110 (1-2 x)^2+967113 (1-2 x)+784\right )}{3773 (3 (1-2 x)-7)^3 \sqrt {1-2 x}}+\frac {40140}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {1250}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

(-2*(784 + 967113*(1 - 2*x) - 817110*(1 - 2*x)^2 + 172665*(1 - 2*x)^3))/(3773*(-7 + 3*(1 - 2*x))^3*Sqrt[1 - 2*
x]) + (40140*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*
x]])/11

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fricas [A]  time = 1.34, size = 162, normalized size = 1.23 \begin {gather*} \frac {1500625 \, \sqrt {11} \sqrt {5} {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 2428470 \, \sqrt {7} \sqrt {3} {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (-\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \, {\left (345330 \, x^{3} + 299115 \, x^{2} - 74556 \, x - 80863\right )} \sqrt {-2 \, x + 1}}{290521 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x),x, algorithm="fricas")

[Out]

1/290521*(1500625*sqrt(11)*sqrt(5)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1)
+ 5*x - 8)/(5*x + 3)) + 2428470*sqrt(7)*sqrt(3)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(-(sqrt(7)*sqrt(3)*sq
rt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(345330*x^3 + 299115*x^2 - 74556*x - 80863)*sqrt(-2*x + 1))/(54*x^4 +
81*x^3 + 18*x^2 - 20*x - 8)

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giac [A]  time = 1.24, size = 132, normalized size = 1.00 \begin {gather*} \frac {625}{121} \, \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 {20070}{2401} \, \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 {32}{26411 \, \sqrt {-2 \, x + 1}} + \frac {9 \, {\left (12213 \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - 57806 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 68453 \, \sqrt {-2 \, x + 1}\right )}}{9604 \, {\left (3 \, x + 2\right )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x),x, algorithm="giac")

[Out]

625/121*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 20070/2401*sqrt
(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 32/26411/sqrt(-2*x + 1) + 9/
9604*(12213*(2*x - 1)^2*sqrt(-2*x + 1) - 57806*(-2*x + 1)^(3/2) + 68453*sqrt(-2*x + 1))/(3*x + 2)^3

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maple [A]  time = 0.01, size = 84, normalized size = 0.64 \begin {gather*} \frac {40140 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{2401}-\frac {1250 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{121}+\frac {32}{26411 \sqrt {-2 x +1}}-\frac {486 \left (\frac {1357 \left (-2 x +1\right )^{\frac {5}{2}}}{3}-\frac {57806 \left (-2 x +1\right )^{\frac {3}{2}}}{27}+\frac {68453 \sqrt {-2 x +1}}{27}\right )}{2401 \left (-6 x -4\right )^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(-2*x+1)^(3/2)/(3*x+2)^4/(5*x+3),x)

[Out]

32/26411/(-2*x+1)^(1/2)-1250/121*arctanh(1/11*55^(1/2)*(-2*x+1)^(1/2))*55^(1/2)-486/2401*(1357/3*(-2*x+1)^(5/2
)-57806/27*(-2*x+1)^(3/2)+68453/27*(-2*x+1)^(1/2))/(-6*x-4)^3+40140/2401*arctanh(1/7*21^(1/2)*(-2*x+1)^(1/2))*
21^(1/2)

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maxima [A]  time = 1.34, size = 137, normalized size = 1.04 \begin {gather*} \frac {625}{121} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) - \frac {20070}{2401} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {2 \, {\left (172665 \, {\left (2 \, x - 1\right )}^{3} + 817110 \, {\left (2 \, x - 1\right )}^{2} + 1934226 \, x - 967897\right )}}{3773 \, {\left (27 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - 189 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + 441 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 343 \, \sqrt {-2 \, x + 1}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x),x, algorithm="maxima")

[Out]

625/121*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 20070/2401*sqrt(21)*log(-
(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 2/3773*(172665*(2*x - 1)^3 + 817110*(2*x - 1)^2
+ 1934226*x - 967897)/(27*(-2*x + 1)^(7/2) - 189*(-2*x + 1)^(5/2) + 441*(-2*x + 1)^(3/2) - 343*sqrt(-2*x + 1)
)

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mupad [B]  time = 1.28, size = 101, normalized size = 0.77 \begin {gather*} \frac {40140\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{2401}-\frac {\frac {2924\,x}{77}+\frac {25940\,{\left (2\,x-1\right )}^2}{1617}+\frac {12790\,{\left (2\,x-1\right )}^3}{3773}-\frac {39506}{2079}}{\frac {343\,\sqrt {1-2\,x}}{27}-\frac {49\,{\left (1-2\,x\right )}^{3/2}}{3}+7\,{\left (1-2\,x\right )}^{5/2}-{\left (1-2\,x\right )}^{7/2}}-\frac {1250\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{121} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((1 - 2*x)^(3/2)*(3*x + 2)^4*(5*x + 3)),x)

[Out]

(40140*21^(1/2)*atanh((21^(1/2)*(1 - 2*x)^(1/2))/7))/2401 - ((2924*x)/77 + (25940*(2*x - 1)^2)/1617 + (12790*(
2*x - 1)^3)/3773 - 39506/2079)/((343*(1 - 2*x)^(1/2))/27 - (49*(1 - 2*x)^(3/2))/3 + 7*(1 - 2*x)^(5/2) - (1 - 2
*x)^(7/2)) - (1250*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2))/11))/121

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sympy [C]  time = 27.18, size = 6412, normalized size = 48.58

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)**4/(3+5*x),x)

[Out]

29774452055040*sqrt(2)*I*(x - 1/2)**(23/2)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 107
5960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744
*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4
+ 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 313609484643840*sqrt(2)*I*(x - 1/2)**(21/2)/(1
7566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334743111876096
0*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6
+ 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 820649918147
29*(x - 1/2)**2) + 1468099054743552*sqrt(2)*I*(x - 1/2)**(19/2)/(17566693917696*(x - 1/2)**12 + 20494476237312
0*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)*
*8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 271316911
7140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 4009033876700160*sqrt(2)*
I*(x - 1/2)**(17/2)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)
**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294
115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x -
1/2)**3 + 82064991814729*(x - 1/2)**2) + 7037799689644416*sqrt(2)*I*(x - 1/2)**(15/2)/(17566693917696*(x - 1/2
)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 68343
38534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x
- 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 823
6367148639168*sqrt(2)*I*(x - 1/2)**(13/2)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075
960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*
(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 +
703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 6425771604658560*sqrt(2)*I*(x - 1/2)**(11/2)/(1
7566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334743111876096
0*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6
+ 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 820649918147
29*(x - 1/2)**2) + 3222450338494464*sqrt(2)*I*(x - 1/2)**(9/2)/(17566693917696*(x - 1/2)**12 + 204944762373120
*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**
8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117
140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 942422173238700*sqrt(2)*I*
(x - 1/2)**(7/2)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**1
0 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115
908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2
)**3 + 82064991814729*(x - 1/2)**2) + 122356413906342*sqrt(2)*I*(x - 1/2)**(5/2)/(17566693917696*(x - 1/2)**12
+ 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534
136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/
2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 49715643
824*sqrt(2)*I*(x - 1/2)**(3/2)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 107596000245888
0*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**
7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 7034142155
54820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 181474110720000*sqrt(55)*I*(x - 1/2)**12*atan(sqrt(110)*sq
rt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10
+ 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 93022941159
08640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)
**3 + 82064991814729*(x - 1/2)**2) + 293680588861440*sqrt(21)*I*(x - 1/2)**12*atan(sqrt(42)*sqrt(x - 1/2)/7)/(
17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 33474311187609
60*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**
6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814
729*(x - 1/2)**2) - 146840294430720*sqrt(21)*I*pi*(x - 1/2)**12/(17566693917696*(x - 1/2)**12 + 20494476237312
0*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)*
*8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 271316911
7140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 90737055360000*sqrt(55)*I
*pi*(x - 1/2)**12/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**
10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 930229411
5908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/
2)**3 + 82064991814729*(x - 1/2)**2) - 2117197958400000*sqrt(55)*I*(x - 1/2)**11*atan(sqrt(110)*sqrt(x - 1/2)/
11)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334743111
8760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1
/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 820649
91814729*(x - 1/2)**2) + 3426273536716800*sqrt(21)*I*(x - 1/2)**11*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917
696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2
)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529
410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/
2)**2) - 1713136768358400*sqrt(21)*I*pi*(x - 1/2)**11/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2
)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 95680
73947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x
- 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 1058598979200000*sqrt(55)*I*pi*(x -
1/2)**11/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334
7431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*
(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 +
82064991814729*(x - 1/2)**2) - 11115289281600000*sqrt(55)*I*(x - 1/2)**10*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17
566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960
*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6
+ 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 8206499181472
9*(x - 1/2)**2) + 17987936067763200*sqrt(21)*I*(x - 1/2)**10*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x
- 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 +
6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605
760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2)
- 8993968033881600*sqrt(21)*I*pi*(x - 1/2)**10/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11
+ 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 95680739477
91744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2
)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 5557644640800000*sqrt(55)*I*pi*(x - 1/2)*
*10/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334743111
8760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1
/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 820649
91814729*(x - 1/2)**2) - 34580899987200000*sqrt(55)*I*(x - 1/2)**9*atan(sqrt(110)*sqrt(x - 1/2)/11)/(175666939
17696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1
/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 62015
29410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x -
1/2)**2) + 55962467766374400*sqrt(21)*I*(x - 1/2)**9*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)*
*12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338
534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x -
1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 27981
233883187200*sqrt(21)*I*pi*(x - 1/2)**9/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 107596
0002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x
- 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 7
03414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 17290449993600000*sqrt(55)*I*pi*(x - 1/2)**9/(175
66693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*
(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 +
6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729
*(x - 1/2)**2) - 70602670807200000*sqrt(55)*I*(x - 1/2)**8*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x
- 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 +
6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605
760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2)
+ 114256705023014400*sqrt(21)*I*(x - 1/2)**8*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 2
04944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 68343385341369
60*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**
5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 571283525115
07200*sqrt(21)*I*pi*(x - 1/2)**8/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458
880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)
**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 70341421
5554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 35301335403600000*sqrt(55)*I*pi*(x - 1/2)**8/(1756669391
7696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/
2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 620152
9410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1
/2)**2) - 98843739130080000*sqrt(55)*I*(x - 1/2)**7*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)
**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 683433
8534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x
- 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 1599
59387032220160*sqrt(21)*I*(x - 1/2)**7*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 20494476
2373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x -
1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 271
3169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 79979693516110080*s
qrt(21)*I*pi*(x - 1/2)**7/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x
- 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9
302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820
*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 49421869565040000*sqrt(55)*I*pi*(x - 1/2)**7/(17566693917696*(x
- 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 +
6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605
760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2)
- 96098079709800000*sqrt(55)*I*(x - 1/2)**6*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 +
204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136
960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)*
*5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 15551607072
5769600*sqrt(21)*I*(x - 1/2)**6*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 204944762373120
*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**
8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117
140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 77758035362884800*sqrt(21)
*I*pi*(x - 1/2)**6/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)*
*10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 93022941
15908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1
/2)**3 + 82064991814729*(x - 1/2)**2) + 48049039854900000*sqrt(55)*I*pi*(x - 1/2)**6/(17566693917696*(x - 1/2)
**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 683433
8534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x
- 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 6406
5386473200000*sqrt(55)*I*(x - 1/2)**5*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 + 2049447
62373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x
- 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 27
13169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 103677380483846400
*sqrt(21)*I*(x - 1/2)**5*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1
/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 956
8073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*
(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 51838690241923200*sqrt(21)*I*pi*(
x - 1/2)**5/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3
347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 930229411590864
0*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3
+ 82064991814729*(x - 1/2)**2) + 32032693236600000*sqrt(55)*I*pi*(x - 1/2)**5/(17566693917696*(x - 1/2)**12 +
204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136
960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)*
*5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 28028606582
025000*sqrt(55)*I*(x - 1/2)**4*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 + 20494476237312
0*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)*
*8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 271316911
7140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 45358853961682800*sqrt(21
)*I*(x - 1/2)**4*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11
+ 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 95680739477
91744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2
)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 22679426980841400*sqrt(21)*I*pi*(x - 1/2)
**4/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 334743111
8760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1
/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 820649
91814729*(x - 1/2)**2) + 14014303291012500*sqrt(55)*I*pi*(x - 1/2)**4/(17566693917696*(x - 1/2)**12 + 20494476
2373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x -
1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 271
3169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 7266675780525000*sq
rt(55)*I*(x - 1/2)**3*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/
2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568
073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(
x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 11759702878954800*sqrt(21)*I*(x -
1/2)**3*atan(sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960
002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x
- 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 70
3414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 5879851439477400*sqrt(21)*I*pi*(x - 1/2)**3/(17566
693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x
- 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6
201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(
x - 1/2)**2) + 3633337890262500*sqrt(55)*I*pi*(x - 1/2)**3/(17566693917696*(x - 1/2)**12 + 204944762373120*(x
- 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 +
9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 27131691171400
20*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 847778841061250*sqrt(55)*I*(x
- 1/2)**2*atan(sqrt(110)*sqrt(x - 1/2)/11)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 107
5960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744
*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4
+ 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) + 1371965335878060*sqrt(21)*I*(x - 1/2)**2*atan(
sqrt(42)*sqrt(x - 1/2)/7)/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x
- 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9
302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820
*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) - 685982667939030*sqrt(21)*I*pi*(x - 1/2)**2/(17566693917696*(x -
1/2)**12 + 204944762373120*(x - 1/2)**11 + 1075960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6
834338534136960*(x - 1/2)**8 + 9568073947791744*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 620152941060576
0*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4 + 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2) +
423889420530625*sqrt(55)*I*pi*(x - 1/2)**2/(17566693917696*(x - 1/2)**12 + 204944762373120*(x - 1/2)**11 + 10
75960002458880*(x - 1/2)**10 + 3347431118760960*(x - 1/2)**9 + 6834338534136960*(x - 1/2)**8 + 956807394779174
4*(x - 1/2)**7 + 9302294115908640*(x - 1/2)**6 + 6201529410605760*(x - 1/2)**5 + 2713169117140020*(x - 1/2)**4
+ 703414215554820*(x - 1/2)**3 + 82064991814729*(x - 1/2)**2)

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