3.28.74 \(\int \frac {(-1+x^3)^{2/3} (8-8 x^3+x^6)}{x^6 (-4+x^3) (-2+x^3)} \, dx\)

Optimal. Leaf size=265 \[ \frac {\log \left (\sqrt [3]{2} \sqrt [3]{x^3-1}-x\right )}{6\ 2^{2/3}}-\frac {\log \left (6^{2/3} \sqrt [3]{x^3-1}-3 x\right )}{8 \sqrt [3]{6}}-\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{2} \sqrt [3]{x^3-1}+x}\right )}{2\ 2^{2/3} \sqrt {3}}+\frac {\sqrt [6]{3} \tan ^{-1}\left (\frac {3^{5/6} x}{2\ 2^{2/3} \sqrt [3]{x^3-1}+\sqrt [3]{3} x}\right )}{8 \sqrt [3]{2}}+\frac {\left (x^3-1\right )^{2/3} \left (13 x^3-8\right )}{40 x^5}-\frac {\log \left (\sqrt [3]{2} \sqrt [3]{x^3-1} x+2^{2/3} \left (x^3-1\right )^{2/3}+x^2\right )}{12\ 2^{2/3}}+\frac {\log \left (6^{2/3} \sqrt [3]{x^3-1} x+2 \sqrt [3]{6} \left (x^3-1\right )^{2/3}+3 x^2\right )}{16 \sqrt [3]{6}} \]

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Rubi [C]  time = 0.85, antiderivative size = 173, normalized size of antiderivative = 0.65, number of steps used = 9, number of rules used = 6, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.162, Rules used = {6725, 264, 277, 239, 430, 429} \begin {gather*} \frac {x \left (x^3-1\right )^{2/3} F_1\left (\frac {1}{3};-\frac {2}{3},1;\frac {4}{3};x^3,\frac {x^3}{4}\right )}{16 \left (1-x^3\right )^{2/3}}-\frac {x \left (x^3-1\right )^{2/3} F_1\left (\frac {1}{3};-\frac {2}{3},1;\frac {4}{3};x^3,\frac {x^3}{2}\right )}{4 \left (1-x^3\right )^{2/3}}+\frac {1}{8} \log \left (\sqrt [3]{x^3-1}-x\right )-\frac {\tan ^{-1}\left (\frac {\frac {2 x}{\sqrt [3]{x^3-1}}+1}{\sqrt {3}}\right )}{4 \sqrt {3}}+\frac {\left (x^3-1\right )^{5/3}}{5 x^5}+\frac {\left (x^3-1\right )^{2/3}}{8 x^2} \end {gather*}

Warning: Unable to verify antiderivative.

[In]

Int[((-1 + x^3)^(2/3)*(8 - 8*x^3 + x^6))/(x^6*(-4 + x^3)*(-2 + x^3)),x]

[Out]

(-1 + x^3)^(2/3)/(8*x^2) + (-1 + x^3)^(5/3)/(5*x^5) + (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3
/4])/(16*(1 - x^3)^(2/3)) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(4*(1 - x^3)^(2/3)) -
ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/8

Rule 239

Int[((a_) + (b_.)*(x_)^3)^(-1/3), x_Symbol] :> Simp[ArcTan[(1 + (2*Rt[b, 3]*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sq
rt[3]*Rt[b, 3]), x] - Simp[Log[(a + b*x^3)^(1/3) - Rt[b, 3]*x]/(2*Rt[b, 3]), x] /; FreeQ[{a, b}, x]

Rule 264

Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[((c*x)^(m + 1)*(a + b*x^n)^(p + 1))/(a
*c*(m + 1)), x] /; FreeQ[{a, b, c, m, n, p}, x] && EqQ[(m + 1)/n + p + 1, 0] && NeQ[m, -1]

Rule 277

Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[((c*x)^(m + 1)*(a + b*x^n)^p)/(c*(m +
1)), x] - Dist[(b*n*p)/(c^n*(m + 1)), Int[(c*x)^(m + n)*(a + b*x^n)^(p - 1), x], x] /; FreeQ[{a, b, c}, x] &&
IGtQ[n, 0] && GtQ[p, 0] && LtQ[m, -1] &&  !ILtQ[(m + n*p + n + 1)/n, 0] && IntBinomialQ[a, b, c, n, m, p, x]

Rule 429

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Simp[a^p*c^q*x*AppellF1[1/n, -p,
-q, 1 + 1/n, -((b*x^n)/a), -((d*x^n)/c)], x] /; FreeQ[{a, b, c, d, n, p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[n
, -1] && (IntegerQ[p] || GtQ[a, 0]) && (IntegerQ[q] || GtQ[c, 0])

Rule 430

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Dist[(a^IntPart[p]*(a + b*x^n)^F
racPart[p])/(1 + (b*x^n)/a)^FracPart[p], Int[(1 + (b*x^n)/a)^p*(c + d*x^n)^q, x], x] /; FreeQ[{a, b, c, d, n,
p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[n, -1] &&  !(IntegerQ[p] || GtQ[a, 0])

Rule 6725

Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionExpand[u/(a + b*x^n), x]}, Int[v, x]
/; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ[n, 0]

Rubi steps

\begin {align*} \int \frac {\left (-1+x^3\right )^{2/3} \left (8-8 x^3+x^6\right )}{x^6 \left (-4+x^3\right ) \left (-2+x^3\right )} \, dx &=\int \left (\frac {\left (-1+x^3\right )^{2/3}}{x^6}-\frac {\left (-1+x^3\right )^{2/3}}{4 x^3}-\frac {\left (-1+x^3\right )^{2/3}}{4 \left (-4+x^3\right )}+\frac {\left (-1+x^3\right )^{2/3}}{2 \left (-2+x^3\right )}\right ) \, dx\\ &=-\left (\frac {1}{4} \int \frac {\left (-1+x^3\right )^{2/3}}{x^3} \, dx\right )-\frac {1}{4} \int \frac {\left (-1+x^3\right )^{2/3}}{-4+x^3} \, dx+\frac {1}{2} \int \frac {\left (-1+x^3\right )^{2/3}}{-2+x^3} \, dx+\int \frac {\left (-1+x^3\right )^{2/3}}{x^6} \, dx\\ &=\frac {\left (-1+x^3\right )^{2/3}}{8 x^2}+\frac {\left (-1+x^3\right )^{5/3}}{5 x^5}-\frac {1}{4} \int \frac {1}{\sqrt [3]{-1+x^3}} \, dx-\frac {\left (-1+x^3\right )^{2/3} \int \frac {\left (1-x^3\right )^{2/3}}{-4+x^3} \, dx}{4 \left (1-x^3\right )^{2/3}}+\frac {\left (-1+x^3\right )^{2/3} \int \frac {\left (1-x^3\right )^{2/3}}{-2+x^3} \, dx}{2 \left (1-x^3\right )^{2/3}}\\ &=\frac {\left (-1+x^3\right )^{2/3}}{8 x^2}+\frac {\left (-1+x^3\right )^{5/3}}{5 x^5}+\frac {x \left (-1+x^3\right )^{2/3} F_1\left (\frac {1}{3};-\frac {2}{3},1;\frac {4}{3};x^3,\frac {x^3}{4}\right )}{16 \left (1-x^3\right )^{2/3}}-\frac {x \left (-1+x^3\right )^{2/3} F_1\left (\frac {1}{3};-\frac {2}{3},1;\frac {4}{3};x^3,\frac {x^3}{2}\right )}{4 \left (1-x^3\right )^{2/3}}-\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{4 \sqrt {3}}+\frac {1}{8} \log \left (-x+\sqrt [3]{-1+x^3}\right )\\ \end {align*}

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Mathematica [A]  time = 0.41, size = 259, normalized size = 0.98 \begin {gather*} \frac {1}{96} \left (8 \sqrt [3]{2} \log \left (\sqrt [3]{2}-\frac {x}{\sqrt [3]{x^3-1}}\right )-2\ 6^{2/3} \log \left (2^{2/3}-\frac {\sqrt [3]{3} x}{\sqrt [3]{x^3-1}}\right )-8 \sqrt [3]{2} \sqrt {3} \tan ^{-1}\left (\frac {\frac {2^{2/3} x}{\sqrt [3]{x^3-1}}+1}{\sqrt {3}}\right )+6\ 2^{2/3} \sqrt [6]{3} \tan ^{-1}\left (\frac {\frac {\sqrt [3]{6} x}{\sqrt [3]{x^3-1}}+1}{\sqrt {3}}\right )-4 \sqrt [3]{2} \log \left (\frac {\sqrt [3]{2} x}{\sqrt [3]{x^3-1}}+\frac {x^2}{\left (x^3-1\right )^{2/3}}+2^{2/3}\right )+6^{2/3} \log \left (\frac {2^{2/3} \sqrt [3]{3} x}{\sqrt [3]{x^3-1}}+\frac {3^{2/3} x^2}{\left (x^3-1\right )^{2/3}}+2 \sqrt [3]{2}\right )\right )+\left (x^3-1\right )^{2/3} \left (\frac {13}{40 x^2}-\frac {1}{5 x^5}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-1 + x^3)^(2/3)*(8 - 8*x^3 + x^6))/(x^6*(-4 + x^3)*(-2 + x^3)),x]

[Out]

(-1/5*1/x^5 + 13/(40*x^2))*(-1 + x^3)^(2/3) + (-8*2^(1/3)*Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(-1 + x^3)^(1/3))/Sq
rt[3]] + 6*2^(2/3)*3^(1/6)*ArcTan[(1 + (6^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + 8*2^(1/3)*Log[2^(1/3) - x/(-1
+ x^3)^(1/3)] - 4*2^(1/3)*Log[2^(2/3) + x^2/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)] - 2*6^(2/3)*Log[2
^(2/3) - (3^(1/3)*x)/(-1 + x^3)^(1/3)] + 6^(2/3)*Log[2*2^(1/3) + (3^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(2/3)*3^(
1/3)*x)/(-1 + x^3)^(1/3)])/96

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IntegrateAlgebraic [A]  time = 0.74, size = 265, normalized size = 1.00 \begin {gather*} \frac {\left (-1+x^3\right )^{2/3} \left (-8+13 x^3\right )}{40 x^5}-\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{x+2 \sqrt [3]{2} \sqrt [3]{-1+x^3}}\right )}{2\ 2^{2/3} \sqrt {3}}+\frac {\sqrt [6]{3} \tan ^{-1}\left (\frac {3^{5/6} x}{\sqrt [3]{3} x+2\ 2^{2/3} \sqrt [3]{-1+x^3}}\right )}{8 \sqrt [3]{2}}+\frac {\log \left (-x+\sqrt [3]{2} \sqrt [3]{-1+x^3}\right )}{6\ 2^{2/3}}-\frac {\log \left (-3 x+6^{2/3} \sqrt [3]{-1+x^3}\right )}{8 \sqrt [3]{6}}-\frac {\log \left (x^2+\sqrt [3]{2} x \sqrt [3]{-1+x^3}+2^{2/3} \left (-1+x^3\right )^{2/3}\right )}{12\ 2^{2/3}}+\frac {\log \left (3 x^2+6^{2/3} x \sqrt [3]{-1+x^3}+2 \sqrt [3]{6} \left (-1+x^3\right )^{2/3}\right )}{16 \sqrt [3]{6}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[((-1 + x^3)^(2/3)*(8 - 8*x^3 + x^6))/(x^6*(-4 + x^3)*(-2 + x^3)),x]

[Out]

((-1 + x^3)^(2/3)*(-8 + 13*x^3))/(40*x^5) - ArcTan[(Sqrt[3]*x)/(x + 2*2^(1/3)*(-1 + x^3)^(1/3))]/(2*2^(2/3)*Sq
rt[3]) + (3^(1/6)*ArcTan[(3^(5/6)*x)/(3^(1/3)*x + 2*2^(2/3)*(-1 + x^3)^(1/3))])/(8*2^(1/3)) + Log[-x + 2^(1/3)
*(-1 + x^3)^(1/3)]/(6*2^(2/3)) - Log[-3*x + 6^(2/3)*(-1 + x^3)^(1/3)]/(8*6^(1/3)) - Log[x^2 + 2^(1/3)*x*(-1 +
x^3)^(1/3) + 2^(2/3)*(-1 + x^3)^(2/3)]/(12*2^(2/3)) + Log[3*x^2 + 6^(2/3)*x*(-1 + x^3)^(1/3) + 2*6^(1/3)*(-1 +
x^3)^(2/3)]/(16*6^(1/3))

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fricas [B]  time = 5.22, size = 552, normalized size = 2.08 \begin {gather*} \frac {30 \cdot 6^{\frac {1}{6}} \sqrt {2} \left (-1\right )^{\frac {1}{3}} x^{5} \arctan \left (\frac {6^{\frac {1}{6}} {\left (24 \cdot 6^{\frac {2}{3}} \sqrt {2} \left (-1\right )^{\frac {2}{3}} {\left (5 \, x^{7} - 22 \, x^{4} + 8 \, x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} - 36 \, \sqrt {2} \left (-1\right )^{\frac {1}{3}} {\left (109 \, x^{8} - 116 \, x^{5} + 16 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}} + 6^{\frac {1}{3}} \sqrt {2} {\left (1189 \, x^{9} - 2064 \, x^{6} + 912 \, x^{3} - 64\right )}\right )}}{6 \, {\left (971 \, x^{9} - 960 \, x^{6} - 48 \, x^{3} + 64\right )}}\right ) + 10 \cdot 6^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} x^{5} \log \left (\frac {18 \cdot 6^{\frac {1}{3}} \left (-1\right )^{\frac {2}{3}} {\left (x^{3} - 1\right )}^{\frac {1}{3}} x^{2} - 6^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} {\left (x^{3} - 4\right )} - 36 \, {\left (x^{3} - 1\right )}^{\frac {2}{3}} x}{x^{3} - 4}\right ) - 5 \cdot 6^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} x^{5} \log \left (-\frac {12 \cdot 6^{\frac {2}{3}} \left (-1\right )^{\frac {1}{3}} {\left (5 \, x^{4} - 2 \, x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} - 6^{\frac {1}{3}} \left (-1\right )^{\frac {2}{3}} {\left (109 \, x^{6} - 116 \, x^{3} + 16\right )} - 18 \, {\left (11 \, x^{5} - 8 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}}}{x^{6} - 8 \, x^{3} + 16}\right ) + 40 \cdot 4^{\frac {1}{6}} \sqrt {3} x^{5} \arctan \left (\frac {4^{\frac {1}{6}} {\left (12 \cdot 4^{\frac {2}{3}} \sqrt {3} {\left (2 \, x^{7} - 5 \, x^{4} + 2 \, x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} + 4^{\frac {1}{3}} \sqrt {3} {\left (91 \, x^{9} - 168 \, x^{6} + 84 \, x^{3} - 8\right )} + 12 \, \sqrt {3} {\left (19 \, x^{8} - 22 \, x^{5} + 4 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}}\right )}}{6 \, {\left (53 \, x^{9} - 48 \, x^{6} - 12 \, x^{3} + 8\right )}}\right ) + 20 \cdot 4^{\frac {2}{3}} x^{5} \log \left (\frac {6 \cdot 4^{\frac {1}{3}} {\left (x^{3} - 1\right )}^{\frac {1}{3}} x^{2} + 4^{\frac {2}{3}} {\left (x^{3} - 2\right )} - 12 \, {\left (x^{3} - 1\right )}^{\frac {2}{3}} x}{x^{3} - 2}\right ) - 10 \cdot 4^{\frac {2}{3}} x^{5} \log \left (\frac {6 \cdot 4^{\frac {2}{3}} {\left (2 \, x^{4} - x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} + 4^{\frac {1}{3}} {\left (19 \, x^{6} - 22 \, x^{3} + 4\right )} + 6 \, {\left (5 \, x^{5} - 4 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}}}{x^{6} - 4 \, x^{3} + 4}\right ) + 36 \, {\left (13 \, x^{3} - 8\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}}}{1440 \, x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x, algorithm="fricas")

[Out]

1/1440*(30*6^(1/6)*sqrt(2)*(-1)^(1/3)*x^5*arctan(1/6*6^(1/6)*(24*6^(2/3)*sqrt(2)*(-1)^(2/3)*(5*x^7 - 22*x^4 +
8*x)*(x^3 - 1)^(2/3) - 36*sqrt(2)*(-1)^(1/3)*(109*x^8 - 116*x^5 + 16*x^2)*(x^3 - 1)^(1/3) + 6^(1/3)*sqrt(2)*(1
189*x^9 - 2064*x^6 + 912*x^3 - 64))/(971*x^9 - 960*x^6 - 48*x^3 + 64)) + 10*6^(2/3)*(-1)^(1/3)*x^5*log((18*6^(
1/3)*(-1)^(2/3)*(x^3 - 1)^(1/3)*x^2 - 6^(2/3)*(-1)^(1/3)*(x^3 - 4) - 36*(x^3 - 1)^(2/3)*x)/(x^3 - 4)) - 5*6^(2
/3)*(-1)^(1/3)*x^5*log(-(12*6^(2/3)*(-1)^(1/3)*(5*x^4 - 2*x)*(x^3 - 1)^(2/3) - 6^(1/3)*(-1)^(2/3)*(109*x^6 - 1
16*x^3 + 16) - 18*(11*x^5 - 8*x^2)*(x^3 - 1)^(1/3))/(x^6 - 8*x^3 + 16)) + 40*4^(1/6)*sqrt(3)*x^5*arctan(1/6*4^
(1/6)*(12*4^(2/3)*sqrt(3)*(2*x^7 - 5*x^4 + 2*x)*(x^3 - 1)^(2/3) + 4^(1/3)*sqrt(3)*(91*x^9 - 168*x^6 + 84*x^3 -
8) + 12*sqrt(3)*(19*x^8 - 22*x^5 + 4*x^2)*(x^3 - 1)^(1/3))/(53*x^9 - 48*x^6 - 12*x^3 + 8)) + 20*4^(2/3)*x^5*l
og((6*4^(1/3)*(x^3 - 1)^(1/3)*x^2 + 4^(2/3)*(x^3 - 2) - 12*(x^3 - 1)^(2/3)*x)/(x^3 - 2)) - 10*4^(2/3)*x^5*log(
(6*4^(2/3)*(2*x^4 - x)*(x^3 - 1)^(2/3) + 4^(1/3)*(19*x^6 - 22*x^3 + 4) + 6*(5*x^5 - 4*x^2)*(x^3 - 1)^(1/3))/(x
^6 - 4*x^3 + 4)) + 36*(13*x^3 - 8)*(x^3 - 1)^(2/3))/x^5

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{6} - 8 \, x^{3} + 8\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}}}{{\left (x^{3} - 2\right )} {\left (x^{3} - 4\right )} x^{6}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x, algorithm="giac")

[Out]

integrate((x^6 - 8*x^3 + 8)*(x^3 - 1)^(2/3)/((x^3 - 2)*(x^3 - 4)*x^6), x)

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maple [F]  time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{3}-1\right )^{\frac {2}{3}} \left (x^{6}-8 x^{3}+8\right )}{x^{6} \left (x^{3}-4\right ) \left (x^{3}-2\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x)

[Out]

int((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{6} - 8 \, x^{3} + 8\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}}}{{\left (x^{3} - 2\right )} {\left (x^{3} - 4\right )} x^{6}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x, algorithm="maxima")

[Out]

integrate((x^6 - 8*x^3 + 8)*(x^3 - 1)^(2/3)/((x^3 - 2)*(x^3 - 4)*x^6), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (x^3-1\right )}^{2/3}\,\left (x^6-8\,x^3+8\right )}{x^6\,\left (x^3-2\right )\,\left (x^3-4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^3 - 1)^(2/3)*(x^6 - 8*x^3 + 8))/(x^6*(x^3 - 2)*(x^3 - 4)),x)

[Out]

int(((x^3 - 1)^(2/3)*(x^6 - 8*x^3 + 8))/(x^6*(x^3 - 2)*(x^3 - 4)), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**3-1)**(2/3)*(x**6-8*x**3+8)/x**6/(x**3-4)/(x**3-2),x)

[Out]

Timed out

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