3.13.38 \(\int \frac {(4+3 x) (-1-x+x^4) \sqrt [4]{-1-x+2 x^4}}{x^6 (1+x+x^4)} \, dx\)

Optimal. Leaf size=90 \[ -4 \sqrt [4]{3} \tan ^{-1}\left (\frac {\sqrt [4]{3} x}{\sqrt [4]{2 x^4-x-1}}\right )+4 \sqrt [4]{3} \tanh ^{-1}\left (\frac {\sqrt [4]{3} x}{\sqrt [4]{2 x^4-x-1}}\right )-\frac {4 \sqrt [4]{2 x^4-x-1} \left (12 x^4-x-1\right )}{5 x^5} \]

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Rubi [F]  time = 1.71, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {(4+3 x) \left (-1-x+x^4\right ) \sqrt [4]{-1-x+2 x^4}}{x^6 \left (1+x+x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

-4*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x^6, x] - 3*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x^5, x] + 8*Defer[Int][(-1
- x + 2*x^4)^(1/4)/x^2, x] - 2*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x, x] + 2*Defer[Int][(-1 - x + 2*x^4)^(1/4)/(
1 + x + x^4), x] - 8*Defer[Int][(x^2*(-1 - x + 2*x^4)^(1/4))/(1 + x + x^4), x] + 2*Defer[Int][(x^3*(-1 - x + 2
*x^4)^(1/4))/(1 + x + x^4), x]

Rubi steps

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

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Mathematica [F]  time = 0.47, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(4+3 x) \left (-1-x+x^4\right ) \sqrt [4]{-1-x+2 x^4}}{x^6 \left (1+x+x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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IntegrateAlgebraic [A]  time = 2.38, size = 90, normalized size = 1.00 \begin {gather*} -\frac {4 \sqrt [4]{-1-x+2 x^4} \left (-1-x+12 x^4\right )}{5 x^5}-4 \sqrt [4]{3} \tan ^{-1}\left (\frac {\sqrt [4]{3} x}{\sqrt [4]{-1-x+2 x^4}}\right )+4 \sqrt [4]{3} \tanh ^{-1}\left (\frac {\sqrt [4]{3} x}{\sqrt [4]{-1-x+2 x^4}}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-4*(-1 - x + 2*x^4)^(1/4)*(-1 - x + 12*x^4))/(5*x^5) - 4*3^(1/4)*ArcTan[(3^(1/4)*x)/(-1 - x + 2*x^4)^(1/4)] +
4*3^(1/4)*ArcTanh[(3^(1/4)*x)/(-1 - x + 2*x^4)^(1/4)]

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fricas [B]  time = 13.77, size = 304, normalized size = 3.38 \begin {gather*} \frac {20 \cdot 3^{\frac {1}{4}} x^{5} \arctan \left (\frac {6 \cdot 3^{\frac {3}{4}} {\left (2 \, x^{4} - x - 1\right )}^{\frac {1}{4}} x^{3} + 6 \cdot 3^{\frac {1}{4}} {\left (2 \, x^{4} - x - 1\right )}^{\frac {3}{4}} x + 3^{\frac {3}{4}} {\left (2 \cdot 3^{\frac {3}{4}} \sqrt {2 \, x^{4} - x - 1} x^{2} + 3^{\frac {1}{4}} {\left (5 \, x^{4} - x - 1\right )}\right )}}{3 \, {\left (x^{4} + x + 1\right )}}\right ) + 5 \cdot 3^{\frac {1}{4}} x^{5} \log \left (\frac {6 \, \sqrt {3} {\left (2 \, x^{4} - x - 1\right )}^{\frac {1}{4}} x^{3} + 6 \cdot 3^{\frac {1}{4}} \sqrt {2 \, x^{4} - x - 1} x^{2} + 3^{\frac {3}{4}} {\left (5 \, x^{4} - x - 1\right )} + 6 \, {\left (2 \, x^{4} - x - 1\right )}^{\frac {3}{4}} x}{x^{4} + x + 1}\right ) - 5 \cdot 3^{\frac {1}{4}} x^{5} \log \left (\frac {6 \, \sqrt {3} {\left (2 \, x^{4} - x - 1\right )}^{\frac {1}{4}} x^{3} - 6 \cdot 3^{\frac {1}{4}} \sqrt {2 \, x^{4} - x - 1} x^{2} - 3^{\frac {3}{4}} {\left (5 \, x^{4} - x - 1\right )} + 6 \, {\left (2 \, x^{4} - x - 1\right )}^{\frac {3}{4}} x}{x^{4} + x + 1}\right ) - 4 \, {\left (12 \, x^{4} - x - 1\right )} {\left (2 \, x^{4} - x - 1\right )}^{\frac {1}{4}}}{5 \, x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*(20*3^(1/4)*x^5*arctan(1/3*(6*3^(3/4)*(2*x^4 - x - 1)^(1/4)*x^3 + 6*3^(1/4)*(2*x^4 - x - 1)^(3/4)*x + 3^(3
/4)*(2*3^(3/4)*sqrt(2*x^4 - x - 1)*x^2 + 3^(1/4)*(5*x^4 - x - 1)))/(x^4 + x + 1)) + 5*3^(1/4)*x^5*log((6*sqrt(
3)*(2*x^4 - x - 1)^(1/4)*x^3 + 6*3^(1/4)*sqrt(2*x^4 - x - 1)*x^2 + 3^(3/4)*(5*x^4 - x - 1) + 6*(2*x^4 - x - 1)
^(3/4)*x)/(x^4 + x + 1)) - 5*3^(1/4)*x^5*log((6*sqrt(3)*(2*x^4 - x - 1)^(1/4)*x^3 - 6*3^(1/4)*sqrt(2*x^4 - x -
1)*x^2 - 3^(3/4)*(5*x^4 - x - 1) + 6*(2*x^4 - x - 1)^(3/4)*x)/(x^4 + x + 1)) - 4*(12*x^4 - x - 1)*(2*x^4 - x
- 1)^(1/4))/x^5

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [C]  time = 11.16, size = 314, normalized size = 3.49

method	result	size
trager	\(-\frac {4 \left (2 x^{4}-x -1\right )^{\frac {1}{4}} \left (12 x^{4}-x -1\right )}{5 x^{5}}-2 \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \ln \left (-\frac {-5 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) x^{4}+6 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} \left (2 x^{4}-x -1\right )^{\frac {1}{4}} x^{3}+6 \sqrt {2 x^{4}-x -1}\, \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) x^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) x -6 \left (2 x^{4}-x -1\right )^{\frac {3}{4}} x +\RootOf \left (\textit {\_Z}^{4}-3\right )^{2} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right )}{x^{4}+x +1}\right )-2 \RootOf \left (\textit {\_Z}^{4}-3\right ) \ln \left (-\frac {5 \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{4}-6 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} \left (2 x^{4}-x -1\right )^{\frac {1}{4}} x^{3}+6 \RootOf \left (\textit {\_Z}^{4}-3\right ) \sqrt {2 x^{4}-x -1}\, x^{2}-\RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x -6 \left (2 x^{4}-x -1\right )^{\frac {3}{4}} x -\RootOf \left (\textit {\_Z}^{4}-3\right )^{3}}{x^{4}+x +1}\right )\)	\(314\)
risch	\(-\frac {4 \left (24 x^{8}-14 x^{5}-14 x^{4}+x^{2}+2 x +1\right )}{5 x^{5} \left (2 x^{4}-x -1\right )^{\frac {3}{4}}}+\frac {\left (-2 \RootOf \left (\textit {\_Z}^{4}-3\right ) \ln \left (\frac {-20 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{12}+8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{9}+24 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{9}-8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{6}+24 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{8}-8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{5}-9 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{6}-12 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{6}+2 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{3}-18 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{5}+6 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {3}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right ) x^{3}+4 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x^{2}-9 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{4}+2 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{4}-3\right )^{3} x +\RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{3}+6 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{3}+3 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{2}+6 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{2}+3 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x +\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}}{\left (2 x^{3}+2 x^{2}+2 x +1\right )^{2} \left (x^{4}+x +1\right ) \left (-1+x \right )^{2}}\right )-2 \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \ln \left (-\frac {-20 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{12}+8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{9}+24 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{9}-8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{6}+24 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{8}-8 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{5}-9 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{6}+12 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{6}+2 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{3}-18 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{5}-6 \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {3}{4}} x^{3}+4 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{2}-9 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{4}+2 \left (8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right )^{\frac {1}{4}} \RootOf \left (\textit {\_Z}^{2}+\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}\right ) \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x +\RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{3}-6 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{3}+3 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x^{2}-6 \sqrt {8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{2}+3 \RootOf \left (\textit {\_Z}^{4}-3\right )^{2} x +\RootOf \left (\textit {\_Z}^{4}-3\right )^{2}}{\left (2 x^{3}+2 x^{2}+2 x +1\right )^{2} \left (x^{4}+x +1\right ) \left (-1+x \right )^{2}}\right )\right ) \left (\left (2 x^{4}-x -1\right )^{3}\right )^{\frac {1}{4}}}{\left (2 x^{4}-x -1\right )^{\frac {3}{4}}}\)	\(1633\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4+3*x)*(x^4-x-1)*(2*x^4-x-1)^(1/4)/x^6/(x^4+x+1),x,method=_RETURNVERBOSE)

[Out]

-4/5*(2*x^4-x-1)^(1/4)*(12*x^4-x-1)/x^5-2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*ln(-(-5*RootOf(_Z^4-3)^2*RootOf(_Z^2+R
ootOf(_Z^4-3)^2)*x^4+6*RootOf(_Z^4-3)^2*(2*x^4-x-1)^(1/4)*x^3+6*(2*x^4-x-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-3)^2
)*x^2+RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x-6*(2*x^4-x-1)^(3/4)*x+RootOf(_Z^4-3)^2*RootOf(_Z^2+Root
Of(_Z^4-3)^2))/(x^4+x+1))-2*RootOf(_Z^4-3)*ln(-(5*RootOf(_Z^4-3)^3*x^4-6*RootOf(_Z^4-3)^2*(2*x^4-x-1)^(1/4)*x^
3+6*RootOf(_Z^4-3)*(2*x^4-x-1)^(1/2)*x^2-RootOf(_Z^4-3)^3*x-6*(2*x^4-x-1)^(3/4)*x-RootOf(_Z^4-3)^3)/(x^4+x+1))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int -\frac {\left (3\,x+4\right )\,\left (-x^4+x+1\right )\,{\left (2\,x^4-x-1\right )}^{1/4}}{x^6\,\left (x^4+x+1\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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