Optimal. Leaf size=174 \[ -\frac {1}{6} \log \left (\sqrt [3]{x^3-1}-x\right )-\frac {1}{2} \log \left (\sqrt [3]{x^3-1}+x\right )-\frac {1}{2} \sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^3-1}-x}\right )+\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^3-1}+x}\right )}{2 \sqrt {3}}-\frac {\left (x^3-1\right )^{2/3}}{x^2}+\frac {1}{4} \log \left (-\sqrt [3]{x^3-1} x+\left (x^3-1\right )^{2/3}+x^2\right )+\frac {1}{12} \log \left (\sqrt [3]{x^3-1} x+\left (x^3-1\right )^{2/3}+x^2\right ) \]
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Rubi [A] time = 0.10, antiderivative size = 143, normalized size of antiderivative = 0.82, number of steps used = 10, number of rules used = 10, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.370, Rules used = {580, 530, 239, 377, 200, 31, 634, 618, 204, 628} \begin {gather*} -\frac {1}{2} \log \left (\frac {x}{\sqrt [3]{x^3-1}}+1\right )-\frac {1}{4} \log \left (\sqrt [3]{x^3-1}-x\right )+\frac {1}{2} \sqrt {3} \tan ^{-1}\left (\frac {1-\frac {2 x}{\sqrt [3]{x^3-1}}}{\sqrt {3}}\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 x}{\sqrt [3]{x^3-1}}+1}{\sqrt {3}}\right )}{2 \sqrt {3}}-\frac {\left (x^3-1\right )^{2/3}}{x^2}+\frac {1}{4} \log \left (-\frac {x}{\sqrt [3]{x^3-1}}+\frac {x^2}{\left (x^3-1\right )^{2/3}}+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 200
Rule 204
Rule 239
Rule 377
Rule 530
Rule 580
Rule 618
Rule 628
Rule 634
Rubi steps
\begin {align*} \int \frac {\left (-2+x^3\right ) \left (-1+x^3\right )^{2/3}}{x^3 \left (-1+2 x^3\right )} \, dx &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}-\frac {1}{2} \int \frac {-2-2 x^3}{\sqrt [3]{-1+x^3} \left (-1+2 x^3\right )} \, dx\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {1}{2} \int \frac {1}{\sqrt [3]{-1+x^3}} \, dx+\frac {3}{2} \int \frac {1}{\sqrt [3]{-1+x^3} \left (-1+2 x^3\right )} \, dx\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{2 \sqrt {3}}-\frac {1}{4} \log \left (-x+\sqrt [3]{-1+x^3}\right )+\frac {3}{2} \operatorname {Subst}\left (\int \frac {1}{-1-x^3} \, dx,x,\frac {x}{\sqrt [3]{-1+x^3}}\right )\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{2 \sqrt {3}}-\frac {1}{4} \log \left (-x+\sqrt [3]{-1+x^3}\right )+\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{-1-x} \, dx,x,\frac {x}{\sqrt [3]{-1+x^3}}\right )+\frac {1}{2} \operatorname {Subst}\left (\int \frac {-2+x}{1-x+x^2} \, dx,x,\frac {x}{\sqrt [3]{-1+x^3}}\right )\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{2 \sqrt {3}}-\frac {1}{2} \log \left (1+\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {1}{4} \log \left (-x+\sqrt [3]{-1+x^3}\right )+\frac {1}{4} \operatorname {Subst}\left (\int \frac {-1+2 x}{1-x+x^2} \, dx,x,\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {3}{4} \operatorname {Subst}\left (\int \frac {1}{1-x+x^2} \, dx,x,\frac {x}{\sqrt [3]{-1+x^3}}\right )\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{2 \sqrt {3}}+\frac {1}{4} \log \left (1+\frac {x^2}{\left (-1+x^3\right )^{2/3}}-\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {1}{2} \log \left (1+\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {1}{4} \log \left (-x+\sqrt [3]{-1+x^3}\right )+\frac {3}{2} \operatorname {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,-1+\frac {2 x}{\sqrt [3]{-1+x^3}}\right )\\ &=-\frac {\left (-1+x^3\right )^{2/3}}{x^2}+\frac {1}{2} \sqrt {3} \tan ^{-1}\left (\frac {1-\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )+\frac {\tan ^{-1}\left (\frac {1+\frac {2 x}{\sqrt [3]{-1+x^3}}}{\sqrt {3}}\right )}{2 \sqrt {3}}+\frac {1}{4} \log \left (1+\frac {x^2}{\left (-1+x^3\right )^{2/3}}-\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {1}{2} \log \left (1+\frac {x}{\sqrt [3]{-1+x^3}}\right )-\frac {1}{4} \log \left (-x+\sqrt [3]{-1+x^3}\right )\\ \end {align*}
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Mathematica [C] time = 0.24, size = 146, normalized size = 0.84 \begin {gather*} \frac {1}{6} \left (-2 \log \left (\frac {x}{\sqrt [3]{1-x^3}}+1\right )-2 \sqrt {3} \tan ^{-1}\left (\frac {\frac {2 x}{\sqrt [3]{1-x^3}}-1}{\sqrt {3}}\right )-\frac {6 \left (x^3-1\right )^{2/3}}{x^2}+\log \left (-\frac {x}{\sqrt [3]{1-x^3}}+\frac {x^2}{\left (1-x^3\right )^{2/3}}+1\right )\right )-\frac {x^4 \sqrt [3]{1-x^3} F_1\left (\frac {4}{3};\frac {1}{3},1;\frac {7}{3};x^3,2 x^3\right )}{4 \sqrt [3]{x^3-1}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.25, size = 174, normalized size = 1.00 \begin {gather*} -\frac {\left (-1+x^3\right )^{2/3}}{x^2}-\frac {1}{2} \sqrt {3} \tan ^{-1}\left (\frac {\sqrt {3} x}{-x+2 \sqrt [3]{-1+x^3}}\right )+\frac {\tan ^{-1}\left (\frac {\sqrt {3} x}{x+2 \sqrt [3]{-1+x^3}}\right )}{2 \sqrt {3}}-\frac {1}{6} \log \left (-x+\sqrt [3]{-1+x^3}\right )-\frac {1}{2} \log \left (x+\sqrt [3]{-1+x^3}\right )+\frac {1}{4} \log \left (x^2-x \sqrt [3]{-1+x^3}+\left (-1+x^3\right )^{2/3}\right )+\frac {1}{12} \log \left (x^2+x \sqrt [3]{-1+x^3}+\left (-1+x^3\right )^{2/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 6.96, size = 214, normalized size = 1.23 \begin {gather*} \frac {2 \, \sqrt {3} x^{2} \arctan \left (\frac {383838 \, \sqrt {3} {\left (x^{10} - 3 \, x^{4} - 2 \, x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} + 13468 \, \sqrt {3} {\left (x^{11} - 3 \, x^{8} + 4 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}} + \sqrt {3} {\left (198653 \, x^{12} + 393594 \, x^{9} + 5568 \, x^{6} - 400090 \, x^{3} - 198189\right )}}{3 \, {\left (185185 \, x^{12} + 370434 \, x^{9} - 96 \, x^{6} - 370322 \, x^{3} - 185193\right )}}\right ) - x^{2} \log \left (\frac {8 \, x^{9} - 12 \, x^{6} + 6 \, x^{3} - 3 \, {\left (x^{10} - 3 \, x^{4} - 2 \, x\right )} {\left (x^{3} - 1\right )}^{\frac {2}{3}} + 3 \, {\left (x^{11} - 3 \, x^{8} + 4 \, x^{2}\right )} {\left (x^{3} - 1\right )}^{\frac {1}{3}} - 1}{8 \, x^{9} - 12 \, x^{6} + 6 \, x^{3} - 1}\right ) - 12 \, {\left (x^{3} - 1\right )}^{\frac {2}{3}}}{12 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} - 1\right )}^{\frac {2}{3}} {\left (x^{3} - 2\right )}}{{\left (2 \, x^{3} - 1\right )} x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 23.73, size = 835, normalized size = 4.80
method | result | size |
trager | \(-\frac {\left (x^{3}-1\right )^{\frac {2}{3}}}{x^{2}}-\frac {\ln \left (\frac {33016196884989482270840140 x^{2} \left (x^{3}-1\right )^{\frac {1}{3}}+279393921796415422876156 x \left (x^{3}-1\right )^{\frac {2}{3}}+8254049221247370567710035 x^{11} \left (x^{3}-1\right )^{\frac {1}{3}}-24762147663742111703130105 x^{8} \left (x^{3}-1\right )^{\frac {1}{3}}+18700889327124136369949940 x^{9}-49803421050130594753656156 x^{6}+39403101898028224175982242 x^{3}-7250695686481463399577082 x^{12}+18845785825826111769772760 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )+28300298612496775796977664 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2}-139696960898207711438078 \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+419090882694623134314234 \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}+3100410598970580503439069-48860088729938611858127568 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{3}+129827490572386253096509632 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{6}+1002891832080354492305395968 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{6}-611993957495242776609641984 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{3}-8026828278127257345063624 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{12}+66032393769978964541680280 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}-64914818082793302850175656 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{11}+194744454248379908550526968 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{8}-198097181309936893625040840 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-132064787539957929083360560 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x -259659272331173211400702624 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{2}-558046513265170797746653312 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{9}-102605316937845350087800336 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{9}+55274020727532765228472000 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{12}}{\left (2 x^{3}-1\right )^{3}}\right )}{6}+\frac {4 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \ln \left (\frac {-33016196884989482270840140 x^{2} \left (x^{3}-1\right )^{\frac {1}{3}}-16228704520698325712543914 x \left (x^{3}-1\right )^{\frac {2}{3}}-8254049221247370567710035 x^{11} \left (x^{3}-1\right )^{\frac {1}{3}}+24762147663742111703130105 x^{8} \left (x^{3}-1\right )^{\frac {1}{3}}+842928816094874669734198 x^{9}+5306305989843145461933312 x^{6}-7033619137578544375323062 x^{3}+2190233071328485822178203 x^{12}-29664743373524966194481896 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )+67191967266579353132732416 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2}+8114352260349162856271957 \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}-24343056781047488568815871 \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-210095773353658826547145872 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{3}+226149429909913341237273120 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{6}+2381115340009405826641204992 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{6}-1453026292139778511495338496 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{3}+48510529199351077964254656 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{12}-66032393769978964541680280 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+1117575687185661691504624 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{11}-3352727061556985074513872 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{8}+198097181309936893625040840 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}+132064787539957929083360560 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x +4470302748742646766018496 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{2}-1324941604537861619586067328 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{9}-53745228207906738229672768 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right ) x^{9}+131234311067537799087368000 \RootOf \left (64 \textit {\_Z}^{2}-8 \textit {\_Z} +1\right )^{2} x^{12}-1748040905508223700350427}{\left (2 x^{3}-1\right )^{3}}\right )}{3}\) | \(835\) |
risch | \(-\frac {\left (x^{3}-1\right )^{\frac {2}{3}}}{x^{2}}+\frac {\ln \left (-\frac {-11+12 x^{2} \left (x^{3}-1\right )^{\frac {1}{3}}-6 x \left (x^{3}-1\right )^{\frac {2}{3}}+3 x^{11} \left (x^{3}-1\right )^{\frac {1}{3}}-9 x^{8} \left (x^{3}-1\right )^{\frac {1}{3}}+22 x^{9}-22 x^{3}+11 x^{12}-16 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )+3 \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}-9 \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-108 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x +216 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{2}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{11}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{8}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-256 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{3}+264 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{6}-208 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{3}+32 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{12}+38 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{12}-192 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{9}-100 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{9}+384 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{6}}{\left (2 x^{3}-1\right )^{3}}\right )}{6}-\frac {\ln \left (-\frac {-11+12 x^{2} \left (x^{3}-1\right )^{\frac {1}{3}}-6 x \left (x^{3}-1\right )^{\frac {2}{3}}+3 x^{11} \left (x^{3}-1\right )^{\frac {1}{3}}-9 x^{8} \left (x^{3}-1\right )^{\frac {1}{3}}+22 x^{9}-22 x^{3}+11 x^{12}-16 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )+3 \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}-9 \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-108 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x +216 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{2}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{11}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{8}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-256 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{3}+264 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{6}-208 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{3}+32 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{12}+38 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{12}-192 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{9}-100 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{9}+384 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{6}}{\left (2 x^{3}-1\right )^{3}}\right ) \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )}{3}+\frac {\RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \ln \left (\frac {19-120 x^{2} \left (x^{3}-1\right )^{\frac {1}{3}}+60 x \left (x^{3}-1\right )^{\frac {2}{3}}-30 x^{11} \left (x^{3}-1\right )^{\frac {1}{3}}+90 x^{8} \left (x^{3}-1\right )^{\frac {1}{3}}+76 x^{9}-228 x^{6}+190 x^{3}-38 x^{12}-16 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )-30 \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+90 \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}-108 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x +216 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{2}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{10}+54 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{11}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {1}{3}} x^{8}-162 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) \left (x^{3}-1\right )^{\frac {2}{3}} x^{4}+256 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{3}+648 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{6}-464 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{3}-32 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{12}+70 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{12}+192 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{9}-292 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right ) x^{9}-384 \RootOf \left (4 \textit {\_Z}^{2}-2 \textit {\_Z} +1\right )^{2} x^{6}}{\left (2 x^{3}-1\right )^{3}}\right )}{3}\) | \(1198\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} - 1\right )}^{\frac {2}{3}} {\left (x^{3} - 2\right )}}{{\left (2 \, x^{3} - 1\right )} x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\left (x^3-1\right )}^{2/3}\,\left (x^3-2\right )}{x^3\,\left (2\,x^3-1\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (\left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac {2}{3}} \left (x^{3} - 2\right )}{x^{3} \left (2 x^{3} - 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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