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

Optimal. Leaf size=71 \[ -\frac {(3 x-1)^{4/3}}{x}+12 \sqrt [3]{3 x-1}+2 \log (x)-6 \log \left (\sqrt [3]{3 x-1}+1\right )+4 \sqrt {3} \tan ^{-1}\left (\frac {1-2 \sqrt [3]{3 x-1}}{\sqrt {3}}\right ) \]

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Rubi [A]  time = 0.03, antiderivative size = 71, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 6, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.462, Rules used = {47, 50, 58, 618, 204, 31} \[ -\frac {(3 x-1)^{4/3}}{x}+12 \sqrt [3]{3 x-1}+2 \log (x)-6 \log \left (\sqrt [3]{3 x-1}+1\right )+4 \sqrt {3} \tan ^{-1}\left (\frac {1-2 \sqrt [3]{3 x-1}}{\sqrt {3}}\right ) \]

Antiderivative was successfully verified.

[In]

Int[(-1 + 3*x)^(4/3)/x^2,x]

[Out]

12*(-1 + 3*x)^(1/3) - (-1 + 3*x)^(4/3)/x + 4*Sqrt[3]*ArcTan[(1 - 2*(-1 + 3*x)^(1/3))/Sqrt[3]] + 2*Log[x] - 6*L
og[1 + (-1 + 3*x)^(1/3)]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 47

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*
(m + 1)), x] - Dist[(d*n)/(b*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1), x], x] /; FreeQ[{a, b, c, d},
x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && LtQ[m, -1] &&  !(IntegerQ[n] &&  !IntegerQ[m]) &&  !(ILeQ[m + n + 2, 0
] && (FractionQ[m] || GeQ[2*n + m + 1, 0])) && IntLinearQ[a, b, c, d, m, n, x]

Rule 50

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*
(m + n + 1)), x] + Dist[(n*(b*c - a*d))/(b*(m + n + 1)), Int[(a + b*x)^m*(c + d*x)^(n - 1), x], x] /; FreeQ[{a
, b, c, d}, x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && NeQ[m + n + 1, 0] &&  !(IGtQ[m, 0] && ( !IntegerQ[n] || (G
tQ[m, 0] && LtQ[m - n, 0]))) &&  !ILtQ[m + n + 2, 0] && IntLinearQ[a, b, c, d, m, n, x]

Rule 58

Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(2/3)), x_Symbol] :> With[{q = Rt[-((b*c - a*d)/b), 3]}, -Sim
p[Log[RemoveContent[a + b*x, x]]/(2*b*q^2), x] + (Dist[3/(2*b*q), Subst[Int[1/(q^2 - q*x + x^2), x], x, (c + d
*x)^(1/3)], x] + Dist[3/(2*b*q^2), Subst[Int[1/(q + x), x], x, (c + d*x)^(1/3)], x])] /; FreeQ[{a, b, c, d}, x
] && NegQ[(b*c - a*d)/b]

Rule 204

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

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rubi steps

\begin {align*} \int \frac {(-1+3 x)^{4/3}}{x^2} \, dx &=-\frac {(-1+3 x)^{4/3}}{x}+4 \int \frac {\sqrt [3]{-1+3 x}}{x} \, dx\\ &=12 \sqrt [3]{-1+3 x}-\frac {(-1+3 x)^{4/3}}{x}-4 \int \frac {1}{x (-1+3 x)^{2/3}} \, dx\\ &=12 \sqrt [3]{-1+3 x}-\frac {(-1+3 x)^{4/3}}{x}+2 \log (x)-6 \operatorname {Subst}\left (\int \frac {1}{1+x} \, dx,x,\sqrt [3]{-1+3 x}\right )-6 \operatorname {Subst}\left (\int \frac {1}{1-x+x^2} \, dx,x,\sqrt [3]{-1+3 x}\right )\\ &=12 \sqrt [3]{-1+3 x}-\frac {(-1+3 x)^{4/3}}{x}+2 \log (x)-6 \log \left (1+\sqrt [3]{-1+3 x}\right )+12 \operatorname {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,-1+2 \sqrt [3]{-1+3 x}\right )\\ &=12 \sqrt [3]{-1+3 x}-\frac {(-1+3 x)^{4/3}}{x}+4 \sqrt {3} \tan ^{-1}\left (\frac {1-2 \sqrt [3]{-1+3 x}}{\sqrt {3}}\right )+2 \log (x)-6 \log \left (1+\sqrt [3]{-1+3 x}\right )\\ \end {align*}

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Mathematica [C]  time = 0.01, size = 26, normalized size = 0.37 \[ \frac {9}{7} (3 x-1)^{7/3} \, _2F_1\left (2,\frac {7}{3};\frac {10}{3};1-3 x\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(-1 + 3*x)^(4/3)/x^2,x]

[Out]

(9*(-1 + 3*x)^(7/3)*Hypergeometric2F1[2, 7/3, 10/3, 1 - 3*x])/7

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IntegrateAlgebraic [A]  time = 0.06, size = 88, normalized size = 1.24 \[ \frac {\sqrt [3]{3 x-1} (9 x+1)}{x}-4 \log \left (\sqrt [3]{3 x-1}+1\right )+2 \log \left ((3 x-1)^{2/3}-\sqrt [3]{3 x-1}+1\right )+4 \sqrt {3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\frac {2 \sqrt [3]{3 x-1}}{\sqrt {3}}\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

((-1 + 3*x)^(1/3)*(1 + 9*x))/x + 4*Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(-1 + 3*x)^(1/3))/Sqrt[3]] - 4*Log[1 + (-1 +
3*x)^(1/3)] + 2*Log[1 - (-1 + 3*x)^(1/3) + (-1 + 3*x)^(2/3)]

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fricas [A]  time = 0.70, size = 80, normalized size = 1.13 \[ -\frac {4 \, \sqrt {3} x \arctan \left (\frac {2}{3} \, \sqrt {3} {\left (3 \, x - 1\right )}^{\frac {1}{3}} - \frac {1}{3} \, \sqrt {3}\right ) - 2 \, x \log \left ({\left (3 \, x - 1\right )}^{\frac {2}{3}} - {\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) + 4 \, x \log \left ({\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) - {\left (9 \, x + 1\right )} {\left (3 \, x - 1\right )}^{\frac {1}{3}}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(4*sqrt(3)*x*arctan(2/3*sqrt(3)*(3*x - 1)^(1/3) - 1/3*sqrt(3)) - 2*x*log((3*x - 1)^(2/3) - (3*x - 1)^(1/3) +
1) + 4*x*log((3*x - 1)^(1/3) + 1) - (9*x + 1)*(3*x - 1)^(1/3))/x

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giac [A]  time = 0.65, size = 76, normalized size = 1.07 \[ -4 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, {\left (3 \, x - 1\right )}^{\frac {1}{3}} - 1\right )}\right ) + 9 \, {\left (3 \, x - 1\right )}^{\frac {1}{3}} + \frac {{\left (3 \, x - 1\right )}^{\frac {1}{3}}}{x} + 2 \, \log \left ({\left (3 \, x - 1\right )}^{\frac {2}{3}} - {\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) - 4 \, \log \left ({\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(3*x - 1)^(1/3) - 1)) + 9*(3*x - 1)^(1/3) + (3*x - 1)^(1/3)/x + 2*log((3*x -
1)^(2/3) - (3*x - 1)^(1/3) + 1) - 4*log((3*x - 1)^(1/3) + 1)

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maple [C]  time = 0.60, size = 67, normalized size = 0.94

method	result	size
meijerg	\(-\frac {4 \mathrm {signum}\left (-\frac {1}{3}+x \right )^{\frac {4}{3}} \left (-\frac {3 \Gamma \left (\frac {2}{3}\right ) x \hypergeom \left (\left [\frac {2}{3}, 1, 1\right ], \left [2, 3\right ], 3 x \right )}{2}+3 \left (2+\frac {\pi \sqrt {3}}{6}-\frac {\ln \relax (3)}{2}+\ln \relax (x )+i \pi \right ) \Gamma \left (\frac {2}{3}\right )+\frac {3 \Gamma \left (\frac {2}{3}\right )}{4 x}\right )}{3 \Gamma \left (\frac {2}{3}\right ) \left (-\mathrm {signum}\left (-\frac {1}{3}+x \right )\right )^{\frac {4}{3}}}\)	\(67\)
derivativedivides	\(9 \left (-1+3 x \right )^{\frac {1}{3}}-\frac {1}{1+\left (-1+3 x \right )^{\frac {1}{3}}}-4 \ln \left (1+\left (-1+3 x \right )^{\frac {1}{3}}\right )+\frac {1+\left (-1+3 x \right )^{\frac {1}{3}}}{\left (-1+3 x \right )^{\frac {2}{3}}-\left (-1+3 x \right )^{\frac {1}{3}}+1}+2 \ln \left (\left (-1+3 x \right )^{\frac {2}{3}}-\left (-1+3 x \right )^{\frac {1}{3}}+1\right )-4 \sqrt {3}\, \arctan \left (\frac {\left (2 \left (-1+3 x \right )^{\frac {1}{3}}-1\right ) \sqrt {3}}{3}\right )\)	\(109\)
default	\(9 \left (-1+3 x \right )^{\frac {1}{3}}-\frac {1}{1+\left (-1+3 x \right )^{\frac {1}{3}}}-4 \ln \left (1+\left (-1+3 x \right )^{\frac {1}{3}}\right )+\frac {1+\left (-1+3 x \right )^{\frac {1}{3}}}{\left (-1+3 x \right )^{\frac {2}{3}}-\left (-1+3 x \right )^{\frac {1}{3}}+1}+2 \ln \left (\left (-1+3 x \right )^{\frac {2}{3}}-\left (-1+3 x \right )^{\frac {1}{3}}+1\right )-4 \sqrt {3}\, \arctan \left (\frac {\left (2 \left (-1+3 x \right )^{\frac {1}{3}}-1\right ) \sqrt {3}}{3}\right )\)	\(109\)
risch	\(\frac {\left (-1+3 x \right )^{\frac {1}{3}}}{x}+\frac {\left (-\frac {4 \left (-1+3 x \right )^{\frac {2}{3}} \left (-\mathrm {signum}\left (-\frac {1}{3}+x \right )\right )^{\frac {2}{3}} \left (2 \Gamma \left (\frac {2}{3}\right ) x \hypergeom \left (\left [1, 1, \frac {5}{3}\right ], \left [2, 2\right ], 3 x \right )+\left (\frac {\pi \sqrt {3}}{6}-\frac {\ln \relax (3)}{2}+\ln \relax (x )+i \pi \right ) \Gamma \left (\frac {2}{3}\right )\right )}{\left (\left (-1+3 x \right )^{2}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \mathrm {signum}\left (-\frac {1}{3}+x \right )^{\frac {2}{3}}}+\frac {9 \left (-1+3 x \right )^{\frac {2}{3}} \left (-\mathrm {signum}\left (-\frac {1}{3}+x \right )\right )^{\frac {2}{3}} x \hypergeom \left (\left [\frac {2}{3}, 1\right ], \relax [2], 3 x \right )}{\left (\left (-1+3 x \right )^{2}\right )^{\frac {1}{3}} \mathrm {signum}\left (-\frac {1}{3}+x \right )^{\frac {2}{3}}}\right ) \left (\left (-1+3 x \right )^{2}\right )^{\frac {1}{3}}}{\left (-1+3 x \right )^{\frac {2}{3}}}\)	\(146\)
trager	\(\frac {\left (1+9 x \right ) \left (-1+3 x \right )^{\frac {1}{3}}}{x}-4 \ln \left (\frac {\left (-1+3 x \right )^{\frac {2}{3}} \RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )+\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )^{2} x -\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )^{2}+\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right ) x +\left (-1+3 x \right )^{\frac {1}{3}}}{x}\right )+4 \RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right ) \ln \left (-\frac {\left (-1+3 x \right )^{\frac {2}{3}} \RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )+\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )^{2} x -\left (-1+3 x \right )^{\frac {2}{3}}+\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right ) \left (-1+3 x \right )^{\frac {1}{3}}-\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )^{2}-2 \RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right ) x +\RootOf \left (\textit {\_Z}^{2}-\textit {\_Z} +1\right )}{x}\right )\)	\(195\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-1+3*x)^(4/3)/x^2,x,method=_RETURNVERBOSE)

[Out]

-4/3/GAMMA(2/3)*signum(-1/3+x)^(4/3)/(-signum(-1/3+x))^(4/3)*(-3/2*GAMMA(2/3)*x*hypergeom([2/3,1,1],[2,3],3*x)
+3*(2+1/6*Pi*3^(1/2)-1/2*ln(3)+ln(x)+I*Pi)*GAMMA(2/3)+3/4*GAMMA(2/3)/x)

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maxima [A]  time = 1.09, size = 76, normalized size = 1.07 \[ -4 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, {\left (3 \, x - 1\right )}^{\frac {1}{3}} - 1\right )}\right ) + 9 \, {\left (3 \, x - 1\right )}^{\frac {1}{3}} + \frac {{\left (3 \, x - 1\right )}^{\frac {1}{3}}}{x} + 2 \, \log \left ({\left (3 \, x - 1\right )}^{\frac {2}{3}} - {\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) - 4 \, \log \left ({\left (3 \, x - 1\right )}^{\frac {1}{3}} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(3*x - 1)^(1/3) - 1)) + 9*(3*x - 1)^(1/3) + (3*x - 1)^(1/3)/x + 2*log((3*x -
1)^(2/3) - (3*x - 1)^(1/3) + 1) - 4*log((3*x - 1)^(1/3) + 1)

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mupad [B]  time = 0.21, size = 90, normalized size = 1.27 \[ 9\,{\left (3\,x-1\right )}^{1/3}-4\,\ln \left (144\,{\left (3\,x-1\right )}^{1/3}+144\right )+\frac {{\left (3\,x-1\right )}^{1/3}}{x}+\ln \left (18-36\,{\left (3\,x-1\right )}^{1/3}+\sqrt {3}\,18{}\mathrm {i}\right )\,\left (2+\sqrt {3}\,2{}\mathrm {i}\right )-\ln \left (36\,{\left (3\,x-1\right )}^{1/3}-18+\sqrt {3}\,18{}\mathrm {i}\right )\,\left (-2+\sqrt {3}\,2{}\mathrm {i}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x - 1)^(4/3)/x^2,x)

[Out]

9*(3*x - 1)^(1/3) - 4*log(144*(3*x - 1)^(1/3) + 144) + (3*x - 1)^(1/3)/x + log(3^(1/2)*18i - 36*(3*x - 1)^(1/3
) + 18)*(3^(1/2)*2i + 2) - log(3^(1/2)*18i + 36*(3*x - 1)^(1/3) - 18)*(3^(1/2)*2i - 2)

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sympy [C]  time = 2.27, size = 541, normalized size = 7.62 \[ \frac {189 \sqrt [3]{3} \left (x - \frac {1}{3}\right )^{\frac {4}{3}} e^{\frac {i \pi }{3}} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} + \frac {84 \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{\frac {i \pi }{3}} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} + \frac {84 \left (x - \frac {1}{3}\right ) \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{\frac {i \pi }{3}} + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} - \frac {84 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{i \pi } + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} + \frac {84 \left (x - \frac {1}{3}\right ) e^{\frac {2 i \pi }{3}} \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{\frac {5 i \pi }{3}} + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} + \frac {28 \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{\frac {i \pi }{3}} + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} - \frac {28 e^{\frac {i \pi }{3}} \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{i \pi } + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} + \frac {28 e^{\frac {2 i \pi }{3}} \log {\left (- \sqrt [3]{3} \sqrt [3]{x - \frac {1}{3}} e^{\frac {5 i \pi }{3}} + 1 \right )} \Gamma \left (\frac {7}{3}\right )}{9 \left (x - \frac {1}{3}\right ) e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right ) + 3 e^{\frac {i \pi }{3}} \Gamma \left (\frac {10}{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1+3*x)**(4/3)/x**2,x)

[Out]

189*3**(1/3)*(x - 1/3)**(4/3)*exp(I*pi/3)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamm
a(10/3)) + 84*3**(1/3)*(x - 1/3)**(1/3)*exp(I*pi/3)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*
pi/3)*gamma(10/3)) + 84*(x - 1/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3
)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) - 84*(x - 1/3)*exp(I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/
3)*exp_polar(I*pi) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 84*(x -
1/3)*exp(2*I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(5*I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3
)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 28*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi/3) + 1)*gamma(7/
3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) - 28*exp(I*pi/3)*log(-3**(1/3)*(x - 1/3)*
*(1/3)*exp_polar(I*pi) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 28*
exp(2*I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(5*I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamm
a(10/3) + 3*exp(I*pi/3)*gamma(10/3))

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