Integrand size = 24, antiderivative size = 257 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=-\frac {\left (-x^2+x^3\right )^{2/3}}{2 (-1+x) x}+\frac {\arctan \left (\frac {\sqrt {3} x}{x+2^{2/3} \sqrt [3]{-x^2+x^3}}\right )}{2 \sqrt [3]{2} \sqrt {3}}-\frac {\log \left (-2 x+2^{2/3} \sqrt [3]{-x^2+x^3}\right )}{6 \sqrt [3]{2}}+\frac {\log \left (2 x^2+2^{2/3} x \sqrt [3]{-x^2+x^3}+\sqrt [3]{2} \left (-x^2+x^3\right )^{2/3}\right )}{12 \sqrt [3]{2}}+\frac {1}{6} \text {RootSum}\left [3-3 \text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log (x)+\log \left (\sqrt [3]{-x^2+x^3}-x \text {$\#$1}\right )}{\text {$\#$1}}\&\right ]-\frac {1}{6} \text {RootSum}\left [1-\text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log (x)+\log \left (\sqrt [3]{-x^2+x^3}-x \text {$\#$1}\right )}{\text {$\#$1}}\&\right ] \]
Time = 0.47 (sec) , antiderivative size = 281, normalized size of antiderivative = 1.09 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\frac {x^{2/3} \left (-12 \sqrt [3]{x}+2\ 2^{2/3} \sqrt {3} \sqrt [3]{-1+x} \arctan \left (\frac {\sqrt {3} \sqrt [3]{x}}{2^{2/3} \sqrt [3]{-1+x}+\sqrt [3]{x}}\right )-2\ 2^{2/3} \sqrt [3]{-1+x} \log \left (2^{2/3} \sqrt [3]{-1+x}-2 \sqrt [3]{x}\right )+2^{2/3} \sqrt [3]{-1+x} \log \left (\sqrt [3]{2} (-1+x)^{2/3}+2^{2/3} \sqrt [3]{-1+x} \sqrt [3]{x}+2 x^{2/3}\right )+4 \sqrt [3]{-1+x} \text {RootSum}\left [3-3 \text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log \left (\sqrt [3]{x}\right )+\log \left (\sqrt [3]{-1+x}-\sqrt [3]{x} \text {$\#$1}\right )}{\text {$\#$1}}\&\right ]-4 \sqrt [3]{-1+x} \text {RootSum}\left [1-\text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log \left (\sqrt [3]{x}\right )+\log \left (\sqrt [3]{-1+x}-\sqrt [3]{x} \text {$\#$1}\right )}{\text {$\#$1}}\&\right ]\right )}{24 \sqrt [3]{(-1+x) x^2}} \]
(x^(2/3)*(-12*x^(1/3) + 2*2^(2/3)*Sqrt[3]*(-1 + x)^(1/3)*ArcTan[(Sqrt[3]*x ^(1/3))/(2^(2/3)*(-1 + x)^(1/3) + x^(1/3))] - 2*2^(2/3)*(-1 + x)^(1/3)*Log [2^(2/3)*(-1 + x)^(1/3) - 2*x^(1/3)] + 2^(2/3)*(-1 + x)^(1/3)*Log[2^(1/3)* (-1 + x)^(2/3) + 2^(2/3)*(-1 + x)^(1/3)*x^(1/3) + 2*x^(2/3)] + 4*(-1 + x)^ (1/3)*RootSum[3 - 3*#1^3 + #1^6 & , (-Log[x^(1/3)] + Log[(-1 + x)^(1/3) - x^(1/3)*#1])/#1 & ] - 4*(-1 + x)^(1/3)*RootSum[1 - #1^3 + #1^6 & , (-Log[x ^(1/3)] + Log[(-1 + x)^(1/3) - x^(1/3)*#1])/#1 & ]))/(24*((-1 + x)*x^2)^(1 /3))
Result contains complex when optimal does not.
Time = 2.04 (sec) , antiderivative size = 1274, normalized size of antiderivative = 4.96, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {2467, 25, 2035, 7276, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x^3}{\sqrt [3]{x^3-x^2} \left (x^6-1\right )} \, dx\) |
| \(\Big \downarrow \) 2467 |
| \(\displaystyle \frac {\sqrt [3]{x-1} x^{2/3} \int -\frac {x^{7/3}}{\sqrt [3]{x-1} \left (1-x^6\right )}dx}{\sqrt [3]{x^3-x^2}}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\sqrt [3]{x-1} x^{2/3} \int \frac {x^{7/3}}{\sqrt [3]{x-1} \left (1-x^6\right )}dx}{\sqrt [3]{x^3-x^2}}\) |
| \(\Big \downarrow \) 2035 |
| \(\displaystyle -\frac {3 \sqrt [3]{x-1} x^{2/3} \int \frac {x^3}{\sqrt [3]{x-1} \left (1-x^6\right )}d\sqrt [3]{x}}{\sqrt [3]{x^3-x^2}}\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle -\frac {3 \sqrt [3]{x-1} x^{2/3} \int \left (\frac {\sqrt [3]{x}-2}{18 \left (x^{2/3}-\sqrt [3]{x}+1\right ) \sqrt [3]{x-1}}-\frac {\sqrt [3]{x}}{9 \left (x^{2/3}-1\right ) \sqrt [3]{x-1}}+\frac {\sqrt [3]{x}+2}{18 \left (x^{2/3}+\sqrt [3]{x}+1\right ) \sqrt [3]{x-1}}+\frac {x-2}{6 \sqrt [3]{x-1} \left (x^2-x+1\right )}+\frac {x+2}{6 \sqrt [3]{x-1} \left (x^2+x+1\right )}\right )d\sqrt [3]{x}}{\sqrt [3]{x^3-x^2}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {3 \sqrt [3]{x-1} x^{2/3} \left (-\frac {\arctan \left (\frac {1-\frac {\sqrt [3]{2} \left (1-\sqrt [3]{x}\right )}{\sqrt [3]{x-1}}}{\sqrt {3}}\right )}{18 \sqrt [3]{2} \sqrt {3}}+\frac {\arctan \left (\frac {\frac {2 \sqrt [3]{2} \left (1-\sqrt [3]{x}\right )}{\sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{18 \sqrt [3]{2} \sqrt {3}}-\frac {\arctan \left (\frac {1-2^{2/3} \sqrt [3]{x-1}}{\sqrt {3}}\right )}{18 \sqrt [3]{2} \sqrt {3}}-\frac {\arctan \left (\frac {\frac {2 \sqrt [3]{2} \sqrt [3]{x}}{\sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{9 \sqrt [3]{2} \sqrt {3}}+\frac {\sqrt [3]{\frac {i-\sqrt {3}}{3 i-\sqrt {3}}} \arctan \left (\frac {\frac {2 \sqrt [3]{x}}{\sqrt [3]{\frac {i-\sqrt {3}}{3 i-\sqrt {3}}} \sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{6 \sqrt {3}}-\frac {\sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \arctan \left (\frac {\frac {2 \sqrt [3]{x}}{\sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{6 \sqrt {3}}-\frac {\arctan \left (\frac {\frac {2 \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \sqrt [3]{x}}{\sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{6 \sqrt {3} \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}}}+\frac {\sqrt [3]{\frac {i+\sqrt {3}}{3 i+\sqrt {3}}} \arctan \left (\frac {\frac {2 \sqrt [3]{x}}{\sqrt [3]{\frac {i+\sqrt {3}}{3 i+\sqrt {3}}} \sqrt [3]{x-1}}+1}{\sqrt {3}}\right )}{6 \sqrt {3}}-\frac {\log \left (1-\frac {\sqrt [3]{2} \left (1-\sqrt [3]{x}\right )}{\sqrt [3]{x-1}}\right )}{54 \sqrt [3]{2}}+\frac {\log \left (\frac {2^{2/3} \left (1-\sqrt [3]{x}\right )^2}{(x-1)^{2/3}}+\frac {\sqrt [3]{2} \left (1-\sqrt [3]{x}\right )}{\sqrt [3]{x-1}}+1\right )}{108 \sqrt [3]{2}}-\frac {\log \left (\sqrt [3]{x-1}+\sqrt [3]{2}\right )}{36 \sqrt [3]{2}}+\frac {\log \left (2^{2/3} \sqrt [3]{x-1}-\sqrt [3]{x}+1\right )}{36 \sqrt [3]{2}}-\frac {\log \left (\left (1-\sqrt [3]{x}\right ) \left (\sqrt [3]{x}+1\right )^2\right )}{108 \sqrt [3]{2}}+\frac {\log \left (\sqrt [3]{2} \sqrt [3]{x}-\sqrt [3]{x-1}\right )}{18 \sqrt [3]{2}}-\frac {1}{12} \sqrt [3]{\frac {i-\sqrt {3}}{3 i-\sqrt {3}}} \log \left (\frac {\sqrt [3]{x}}{\sqrt [3]{\frac {i-\sqrt {3}}{3 i-\sqrt {3}}}}-\sqrt [3]{x-1}\right )+\frac {1}{12} \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \log \left (\frac {\sqrt [3]{x}}{\sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}}}-\sqrt [3]{x-1}\right )+\frac {\log \left (\sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \sqrt [3]{x}-\sqrt [3]{x-1}\right )}{12 \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}}}-\frac {1}{12} \sqrt [3]{\frac {i+\sqrt {3}}{3 i+\sqrt {3}}} \log \left (\frac {\sqrt [3]{x}}{\sqrt [3]{\frac {i+\sqrt {3}}{3 i+\sqrt {3}}}}-\sqrt [3]{x-1}\right )-\frac {\log (x+1)}{108 \sqrt [3]{2}}-\frac {1}{36} \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}} \log \left (2 x-i \sqrt {3}-1\right )+\frac {1}{36} \sqrt [3]{\frac {i+\sqrt {3}}{3 i+\sqrt {3}}} \log \left (2 x-i \sqrt {3}+1\right )-\frac {\log \left (2 x+i \sqrt {3}-1\right )}{36 \sqrt [3]{-\frac {i-\sqrt {3}}{i+\sqrt {3}}}}+\frac {1}{36} \sqrt [3]{\frac {i-\sqrt {3}}{3 i-\sqrt {3}}} \log \left (2 x+i \sqrt {3}+1\right )+\frac {\sqrt [3]{x}}{6 \sqrt [3]{x-1}}\right )}{\sqrt [3]{x^3-x^2}}\) |
(-3*(-1 + x)^(1/3)*x^(2/3)*(x^(1/3)/(6*(-1 + x)^(1/3)) - ArcTan[(1 - (2^(1 /3)*(1 - x^(1/3)))/(-1 + x)^(1/3))/Sqrt[3]]/(18*2^(1/3)*Sqrt[3]) + ArcTan[ (1 + (2*2^(1/3)*(1 - x^(1/3)))/(-1 + x)^(1/3))/Sqrt[3]]/(18*2^(1/3)*Sqrt[3 ]) - ArcTan[(1 - 2^(2/3)*(-1 + x)^(1/3))/Sqrt[3]]/(18*2^(1/3)*Sqrt[3]) - A rcTan[(1 + (2*2^(1/3)*x^(1/3))/(-1 + x)^(1/3))/Sqrt[3]]/(9*2^(1/3)*Sqrt[3] ) + (((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)*ArcTan[(1 + (2*x^(1/3))/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)*(-1 + x)^(1/3)))/Sqrt[3]])/(6*Sqrt[3]) - ( (-((I - Sqrt[3])/(I + Sqrt[3])))^(1/3)*ArcTan[(1 + (2*x^(1/3))/((-((I - Sq rt[3])/(I + Sqrt[3])))^(1/3)*(-1 + x)^(1/3)))/Sqrt[3]])/(6*Sqrt[3]) - ArcT an[(1 + (2*(-((I - Sqrt[3])/(I + Sqrt[3])))^(1/3)*x^(1/3))/(-1 + x)^(1/3)) /Sqrt[3]]/(6*Sqrt[3]*(-((I - Sqrt[3])/(I + Sqrt[3])))^(1/3)) + (((I + Sqrt [3])/(3*I + Sqrt[3]))^(1/3)*ArcTan[(1 + (2*x^(1/3))/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/3)*(-1 + x)^(1/3)))/Sqrt[3]])/(6*Sqrt[3]) - Log[1 - (2^(1/3) *(1 - x^(1/3)))/(-1 + x)^(1/3)]/(54*2^(1/3)) + Log[1 + (2^(2/3)*(1 - x^(1/ 3))^2)/(-1 + x)^(2/3) + (2^(1/3)*(1 - x^(1/3)))/(-1 + x)^(1/3)]/(108*2^(1/ 3)) - Log[2^(1/3) + (-1 + x)^(1/3)]/(36*2^(1/3)) + Log[1 + 2^(2/3)*(-1 + x )^(1/3) - x^(1/3)]/(36*2^(1/3)) - Log[(1 - x^(1/3))*(1 + x^(1/3))^2]/(108* 2^(1/3)) + Log[-(-1 + x)^(1/3) + 2^(1/3)*x^(1/3)]/(18*2^(1/3)) - (((I - Sq rt[3])/(3*I - Sqrt[3]))^(1/3)*Log[-(-1 + x)^(1/3) + x^(1/3)/((I - Sqrt[3]) /(3*I - Sqrt[3]))^(1/3)])/12 + ((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/3)*...
3.28.52.3.1 Defintions of rubi rules used
Int[(Fx_)*(x_)^(m_), x_Symbol] :> With[{k = Denominator[m]}, Simp[k Subst [Int[x^(k*(m + 1) - 1)*SubstPower[Fx, x, k], x], x, x^(1/k)], x]] /; Fracti onQ[m] && AlgebraicFunctionQ[Fx, x]
Int[(Fx_.)*(Px_)^(p_), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Simp[Px^F racPart[p]/(x^(r*FracPart[p])*ExpandToSum[Px/x^r, x]^FracPart[p]) Int[x^( p*r)*ExpandToSum[Px/x^r, x]^p*Fx, x], x] /; IGtQ[r, 0]] /; FreeQ[p, x] && P olyQ[Px, x] && !IntegerQ[p] && !MonomialQ[Px, x] && !PolyQ[Fx, x]
Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionE xpand[u/(a + b*x^n), x]}, Int[v, x] /; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ [n, 0]
Time = 0.72 (sec) , antiderivative size = 237, normalized size of antiderivative = 0.92
| method | result | size |
| pseudoelliptic | \(\frac {-2 \sqrt {3}\, 2^{\frac {2}{3}} \arctan \left (\frac {\sqrt {3}\, \left (2^{\frac {2}{3}} \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}+x \right )}{3 x}\right ) \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}-2 \,2^{\frac {2}{3}} \ln \left (\frac {-2^{\frac {1}{3}} x +\left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}}{x}\right ) \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}+2^{\frac {2}{3}} \ln \left (\frac {2^{\frac {2}{3}} x^{2}+2^{\frac {1}{3}} \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}} x +\left (\left (-1+x \right ) x^{2}\right )^{\frac {2}{3}}}{x^{2}}\right ) \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}-4 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{6}-\textit {\_Z}^{3}+1\right )}{\sum }\frac {\ln \left (\frac {-\textit {\_R} x +\left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}}{x}\right )}{\textit {\_R}}\right ) \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}+4 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{6}-3 \textit {\_Z}^{3}+3\right )}{\sum }\frac {\ln \left (\frac {-\textit {\_R} x +\left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}}{x}\right )}{\textit {\_R}}\right ) \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}-12 x}{24 \left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}}\) | \(237\) |
1/24*(-2*3^(1/2)*2^(2/3)*arctan(1/3*3^(1/2)*(2^(2/3)*((-1+x)*x^2)^(1/3)+x) /x)*((-1+x)*x^2)^(1/3)-2*2^(2/3)*ln((-2^(1/3)*x+((-1+x)*x^2)^(1/3))/x)*((- 1+x)*x^2)^(1/3)+2^(2/3)*ln((2^(2/3)*x^2+2^(1/3)*((-1+x)*x^2)^(1/3)*x+((-1+ x)*x^2)^(2/3))/x^2)*((-1+x)*x^2)^(1/3)-4*sum(ln((-_R*x+((-1+x)*x^2)^(1/3)) /x)/_R,_R=RootOf(_Z^6-_Z^3+1))*((-1+x)*x^2)^(1/3)+4*sum(ln((-_R*x+((-1+x)* x^2)^(1/3))/x)/_R,_R=RootOf(_Z^6-3*_Z^3+3))*((-1+x)*x^2)^(1/3)-12*x)/((-1+ x)*x^2)^(1/3)
Result contains higher order function than in optimal. Order 3 vs. order 1.
Time = 0.33 (sec) , antiderivative size = 1164, normalized size of antiderivative = 4.53 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\text {Too large to display} \]
-1/72*(6*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^2 - x)*arctan(-1/6*2^(1/6)*(sqrt(6) *2^(1/3)*x - 2*sqrt(6)*(-1)^(1/3)*(x^3 - x^2)^(1/3))/x) - 6*2^(2/3)*(-1)^( 1/3)*(x^2 - x)*log(-(2^(1/3)*(-1)^(2/3)*x - (x^3 - x^2)^(1/3))/x) + 6^(2/3 )*(x^2 + sqrt(-3)*(x^2 - x) - x)*(I*sqrt(3) + 3)^(1/3)*log((6^(1/3)*(sqrt( 3)*(I*sqrt(-3)*x - I*x) - 3*sqrt(-3)*x + 3*x)*(I*sqrt(3) + 3)^(2/3) + 24*( x^3 - x^2)^(1/3))/x) + 6^(2/3)*(x^2 - sqrt(-3)*(x^2 - x) - x)*(I*sqrt(3) + 3)^(1/3)*log((6^(1/3)*(sqrt(3)*(-I*sqrt(-3)*x - I*x) + 3*sqrt(-3)*x + 3*x )*(I*sqrt(3) + 3)^(2/3) + 24*(x^3 - x^2)^(1/3))/x) - 2*6^(2/3)*(x^2 - x)*( I*sqrt(3) + 3)^(1/3)*log((6^(1/3)*(I*sqrt(3)*x - 3*x)*(I*sqrt(3) + 3)^(2/3 ) + 12*(x^3 - x^2)^(1/3))/x) + 6^(2/3)*(x^2 - sqrt(-3)*(x^2 - x) - x)*(-I* sqrt(3) + 3)^(1/3)*log((6^(1/3)*(sqrt(3)*(I*sqrt(-3)*x + I*x) + 3*sqrt(-3) *x + 3*x)*(-I*sqrt(3) + 3)^(2/3) + 24*(x^3 - x^2)^(1/3))/x) + 6^(2/3)*(x^2 + sqrt(-3)*(x^2 - x) - x)*(-I*sqrt(3) + 3)^(1/3)*log((6^(1/3)*(sqrt(3)*(- I*sqrt(-3)*x + I*x) - 3*sqrt(-3)*x + 3*x)*(-I*sqrt(3) + 3)^(2/3) + 24*(x^3 - x^2)^(1/3))/x) - 2*6^(2/3)*(x^2 - x)*(-I*sqrt(3) + 3)^(1/3)*log((6^(1/3 )*(-I*sqrt(3)*x - 3*x)*(-I*sqrt(3) + 3)^(2/3) + 12*(x^3 - x^2)^(1/3))/x) + 3*2^(2/3)*(x^2 - sqrt(-3)*(x^2 - x) - x)*(I*sqrt(3) - 1)^(1/3)*log(((sqrt (3)*2^(1/3)*(I*sqrt(-3)*x + I*x) + 2^(1/3)*(sqrt(-3)*x + x))*(I*sqrt(3) - 1)^(2/3) + 8*(x^3 - x^2)^(1/3))/x) + 3*2^(2/3)*(x^2 + sqrt(-3)*(x^2 - x) - x)*(I*sqrt(3) - 1)^(1/3)*log(((sqrt(3)*2^(1/3)*(-I*sqrt(-3)*x + I*x) -...
Not integrable
Time = 0.76 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.13 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\int \frac {x^{3}}{\sqrt [3]{x^{2} \left (x - 1\right )} \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} - x + 1\right ) \left (x^{2} + x + 1\right )}\, dx \]
Not integrable
Time = 0.30 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.09 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\int { \frac {x^{3}}{{\left (x^{6} - 1\right )} {\left (x^{3} - x^{2}\right )}^{\frac {1}{3}}} \,d x } \]
Exception generated. \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\text {Exception raised: TypeError} \]
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:proot error [1,0,0,1,0,0,1]proot er ror [1,0,0,-1,0,0,1]Invalid _EXT in replace_ext Error: Bad Argument Valuep root erro
Not integrable
Time = 6.58 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.09 \[ \int \frac {x^3}{\sqrt [3]{-x^2+x^3} \left (-1+x^6\right )} \, dx=\int \frac {x^3}{\left (x^6-1\right )\,{\left (x^3-x^2\right )}^{1/3}} \,d x \]