Optimal. Leaf size=146 \[ \frac {3 \log \left (2^{2/3} \sqrt [3]{x^4+1}-x\right )}{16 \sqrt [3]{2}}-\frac {3 \sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{2\ 2^{2/3} \sqrt [3]{x^4+1}+x}\right )}{16 \sqrt [3]{2}}-\frac {3 \log \left (2^{2/3} \sqrt [3]{x^4+1} x+2 \sqrt [3]{2} \left (x^4+1\right )^{2/3}+x^2\right )}{32 \sqrt [3]{2}}+\frac {3 \left (x^4+1\right )^{2/3} \left (8 x^4+15 x^3+8\right )}{80 x^5} \]
________________________________________________________________________________________
Rubi [F] time = 1.44, 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 {\left (-3+x^4\right ) \left (1+x^4\right )^{2/3} \left (2+x^3+2 x^4\right )}{x^6 \left (4-x^3+4 x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (-3+x^4\right ) \left (1+x^4\right )^{2/3} \left (2+x^3+2 x^4\right )}{x^6 \left (4-x^3+4 x^4\right )} \, dx &=\int \left (-\frac {3 \left (1+x^4\right )^{2/3}}{2 x^6}-\frac {9 \left (1+x^4\right )^{2/3}}{8 x^3}+\frac {\left (1+x^4\right )^{2/3}}{2 x^2}+\frac {3 (-3+16 x) \left (1+x^4\right )^{2/3}}{8 \left (4-x^3+4 x^4\right )}\right ) \, dx\\ &=\frac {3}{8} \int \frac {(-3+16 x) \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+\frac {1}{2} \int \frac {\left (1+x^4\right )^{2/3}}{x^2} \, dx-\frac {9}{8} \int \frac {\left (1+x^4\right )^{2/3}}{x^3} \, dx-\frac {3}{2} \int \frac {\left (1+x^4\right )^{2/3}}{x^6} \, dx\\ &=\frac {3 \, _2F_1\left (-\frac {5}{4},-\frac {2}{3};-\frac {1}{4};-x^4\right )}{10 x^5}-\frac {\, _2F_1\left (-\frac {2}{3},-\frac {1}{4};\frac {3}{4};-x^4\right )}{2 x}+\frac {3}{8} \int \left (-\frac {3 \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4}+\frac {16 x \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4}\right ) \, dx-\frac {9}{16} \operatorname {Subst}\left (\int \frac {\left (1+x^2\right )^{2/3}}{x^2} \, dx,x,x^2\right )\\ &=\frac {9 \left (1+x^4\right )^{2/3}}{16 x^2}+\frac {3 \, _2F_1\left (-\frac {5}{4},-\frac {2}{3};-\frac {1}{4};-x^4\right )}{10 x^5}-\frac {\, _2F_1\left (-\frac {2}{3},-\frac {1}{4};\frac {3}{4};-x^4\right )}{2 x}-\frac {3}{4} \operatorname {Subst}\left (\int \frac {1}{\sqrt [3]{1+x^2}} \, dx,x,x^2\right )-\frac {9}{8} \int \frac {\left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+6 \int \frac {x \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx\\ &=\frac {9 \left (1+x^4\right )^{2/3}}{16 x^2}+\frac {3 \, _2F_1\left (-\frac {5}{4},-\frac {2}{3};-\frac {1}{4};-x^4\right )}{10 x^5}-\frac {\, _2F_1\left (-\frac {2}{3},-\frac {1}{4};\frac {3}{4};-x^4\right )}{2 x}-\frac {9}{8} \int \frac {\left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+6 \int \frac {x \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx-\frac {\left (9 \sqrt {x^4}\right ) \operatorname {Subst}\left (\int \frac {x}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{1+x^4}\right )}{8 x^2}\\ &=\frac {9 \left (1+x^4\right )^{2/3}}{16 x^2}+\frac {3 \, _2F_1\left (-\frac {5}{4},-\frac {2}{3};-\frac {1}{4};-x^4\right )}{10 x^5}-\frac {\, _2F_1\left (-\frac {2}{3},-\frac {1}{4};\frac {3}{4};-x^4\right )}{2 x}-\frac {9}{8} \int \frac {\left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+6 \int \frac {x \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+\frac {\left (9 \sqrt {x^4}\right ) \operatorname {Subst}\left (\int \frac {1+\sqrt {3}-x}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{1+x^4}\right )}{8 x^2}-\frac {\left (9 \sqrt {\frac {1}{2} \left (2+\sqrt {3}\right )} \sqrt {x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{1+x^4}\right )}{4 x^2}\\ &=\frac {9 \left (1+x^4\right )^{2/3}}{16 x^2}+\frac {9 x^2}{4 \left (1-\sqrt {3}-\sqrt [3]{1+x^4}\right )}-\frac {9 \sqrt [4]{3} \sqrt {2+\sqrt {3}} \left (1-\sqrt [3]{1+x^4}\right ) \sqrt {\frac {1+\sqrt [3]{1+x^4}+\left (1+x^4\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{1+x^4}\right )^2}} E\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{1+x^4}}{1-\sqrt {3}-\sqrt [3]{1+x^4}}\right )|-7+4 \sqrt {3}\right )}{8 x^2 \sqrt {-\frac {1-\sqrt [3]{1+x^4}}{\left (1-\sqrt {3}-\sqrt [3]{1+x^4}\right )^2}}}+\frac {3\ 3^{3/4} \left (1-\sqrt [3]{1+x^4}\right ) \sqrt {\frac {1+\sqrt [3]{1+x^4}+\left (1+x^4\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{1+x^4}\right )^2}} F\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{1+x^4}}{1-\sqrt {3}-\sqrt [3]{1+x^4}}\right )|-7+4 \sqrt {3}\right )}{2 \sqrt {2} x^2 \sqrt {-\frac {1-\sqrt [3]{1+x^4}}{\left (1-\sqrt {3}-\sqrt [3]{1+x^4}\right )^2}}}+\frac {3 \, _2F_1\left (-\frac {5}{4},-\frac {2}{3};-\frac {1}{4};-x^4\right )}{10 x^5}-\frac {\, _2F_1\left (-\frac {2}{3},-\frac {1}{4};\frac {3}{4};-x^4\right )}{2 x}-\frac {9}{8} \int \frac {\left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx+6 \int \frac {x \left (1+x^4\right )^{2/3}}{4-x^3+4 x^4} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [F] time = 0.34, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-3+x^4\right ) \left (1+x^4\right )^{2/3} \left (2+x^3+2 x^4\right )}{x^6 \left (4-x^3+4 x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 3.36, size = 146, normalized size = 1.00 \begin {gather*} \frac {3 \left (1+x^4\right )^{2/3} \left (8+15 x^3+8 x^4\right )}{80 x^5}-\frac {3 \sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{x+2\ 2^{2/3} \sqrt [3]{1+x^4}}\right )}{16 \sqrt [3]{2}}+\frac {3 \log \left (-x+2^{2/3} \sqrt [3]{1+x^4}\right )}{16 \sqrt [3]{2}}-\frac {3 \log \left (x^2+2^{2/3} x \sqrt [3]{1+x^4}+2 \sqrt [3]{2} \left (1+x^4\right )^{2/3}\right )}{32 \sqrt [3]{2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 112.12, size = 410, normalized size = 2.81 \begin {gather*} -\frac {10 \, \sqrt {3} 2^{\frac {2}{3}} x^{5} \arctan \left (\frac {\sqrt {3} 2^{\frac {1}{6}} {\left (2^{\frac {5}{6}} {\left (64 \, x^{12} + 240 \, x^{11} + 48 \, x^{10} - x^{9} + 192 \, x^{8} + 480 \, x^{7} + 48 \, x^{6} + 192 \, x^{4} + 240 \, x^{3} + 64\right )} + 12 \, \sqrt {2} {\left (16 \, x^{10} + 28 \, x^{9} + x^{8} + 32 \, x^{6} + 28 \, x^{5} + 16 \, x^{2}\right )} {\left (x^{4} + 1\right )}^{\frac {1}{3}} + 48 \cdot 2^{\frac {1}{6}} {\left (8 \, x^{9} + 2 \, x^{8} - x^{7} + 16 \, x^{5} + 2 \, x^{4} + 8 \, x\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}}\right )}}{6 \, {\left (64 \, x^{12} - 48 \, x^{11} - 96 \, x^{10} - x^{9} + 192 \, x^{8} - 96 \, x^{7} - 96 \, x^{6} + 192 \, x^{4} - 48 \, x^{3} + 64\right )}}\right ) - 10 \cdot 2^{\frac {2}{3}} x^{5} \log \left (\frac {6 \cdot 2^{\frac {1}{3}} {\left (x^{4} + 1\right )}^{\frac {1}{3}} x^{2} + 2^{\frac {2}{3}} {\left (4 \, x^{4} - x^{3} + 4\right )} - 12 \, {\left (x^{4} + 1\right )}^{\frac {2}{3}} x}{4 \, x^{4} - x^{3} + 4}\right ) + 5 \cdot 2^{\frac {2}{3}} x^{5} \log \left (\frac {12 \cdot 2^{\frac {2}{3}} {\left (2 \, x^{5} + x^{4} + 2 \, x\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}} + 2^{\frac {1}{3}} {\left (16 \, x^{8} + 28 \, x^{7} + x^{6} + 32 \, x^{4} + 28 \, x^{3} + 16\right )} + 6 \, {\left (8 \, x^{6} + x^{5} + 8 \, x^{2}\right )} {\left (x^{4} + 1\right )}^{\frac {1}{3}}}{16 \, x^{8} - 8 \, x^{7} + x^{6} + 32 \, x^{4} - 8 \, x^{3} + 16}\right ) - 12 \, {\left (8 \, x^{4} + 15 \, x^{3} + 8\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}}}{320 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{4} + x^{3} + 2\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}} {\left (x^{4} - 3\right )}}{{\left (4 \, x^{4} - x^{3} + 4\right )} x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 127.55, size = 665, normalized size = 4.55
method | result | size |
risch | \(\frac {\frac {3}{10} x^{8}+\frac {9}{16} x^{7}+\frac {3}{5} x^{4}+\frac {9}{16} x^{3}+\frac {3}{10}}{x^{5} \left (x^{4}+1\right )^{\frac {1}{3}}}-\frac {3 \ln \left (\frac {\RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{3}+4 \left (x^{4}+1\right )^{\frac {2}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x +4 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{2}-\left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{2}-4 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{4}-4 \left (x^{4}+1\right )^{\frac {2}{3}} x -4 \RootOf \left (\textit {\_Z}^{3}-4\right )}{4 x^{4}-x^{3}+4}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )}{32}-\frac {3 \ln \left (\frac {\RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{3}+4 \left (x^{4}+1\right )^{\frac {2}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x +4 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{2}-\left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{2}-4 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{4}-4 \left (x^{4}+1\right )^{\frac {2}{3}} x -4 \RootOf \left (\textit {\_Z}^{3}-4\right )}{4 x^{4}-x^{3}+4}\right ) \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right )}{8}+\frac {3 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \ln \left (-\frac {\RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{3}+4 \left (x^{4}+1\right )^{\frac {2}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x +4 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+4 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+16 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{2}+2 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{2}+4 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{4}+\RootOf \left (\textit {\_Z}^{3}-4\right ) x^{3}+8 \left (x^{4}+1\right )^{\frac {2}{3}} x +4 \RootOf \left (\textit {\_Z}^{3}-4\right )}{4 x^{4}-x^{3}+4}\right )}{8}\) | \(665\) |
trager | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}} \left (8 x^{4}+15 x^{3}+8\right )}{80 x^{5}}+\frac {3 \RootOf \left (\textit {\_Z}^{3}-4\right ) \ln \left (-\frac {-2676 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{4}-15696 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{4}+5352 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{3}+31392 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{3}+4524 \left (x^{4}+1\right )^{\frac {2}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x -377 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{2}-36336 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right ) \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{2}+7136 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{4}+41856 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{4}-2676 \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )-15696 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+2007 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{3}+11772 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{3}-10604 \left (x^{4}+1\right )^{\frac {2}{3}} x +7136 \RootOf \left (\textit {\_Z}^{3}-4\right )+41856 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )}{4 x^{4}-x^{3}+4}\right )}{32}+\frac {9 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \ln \left (-\frac {208920 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{4}+2738952 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{4}-417840 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} x^{3}-5477904 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{3}+1269180 \left (x^{4}+1\right )^{\frac {2}{3}} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x -105765 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2} x^{2}-3686922 \left (x^{4}+1\right )^{\frac {1}{3}} \RootOf \left (\textit {\_Z}^{3}-4\right ) \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{2}+626760 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{4}+8216856 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{4}+208920 \RootOf \left (\textit {\_Z}^{3}-4\right )^{3} \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )+2738952 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )^{2} \RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+17410 \RootOf \left (\textit {\_Z}^{3}-4\right ) x^{3}+228246 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right ) x^{3}-805914 \left (x^{4}+1\right )^{\frac {2}{3}} x +626760 \RootOf \left (\textit {\_Z}^{3}-4\right )+8216856 \RootOf \left (\RootOf \left (\textit {\_Z}^{3}-4\right )^{2}+12 \textit {\_Z} \RootOf \left (\textit {\_Z}^{3}-4\right )+144 \textit {\_Z}^{2}\right )}{4 x^{4}-x^{3}+4}\right )}{8}\) | \(996\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{4} + x^{3} + 2\right )} {\left (x^{4} + 1\right )}^{\frac {2}{3}} {\left (x^{4} - 3\right )}}{{\left (4 \, x^{4} - x^{3} + 4\right )} x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\left (x^4+1\right )}^{2/3}\,\left (x^4-3\right )\,\left (2\,x^4+x^3+2\right )}{x^6\,\left (4\,x^4-x^3+4\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________