Optimal. Leaf size=682 \[ \frac {\sqrt [3]{-\frac {1}{3}} \left (4-\sqrt [3]{-3} 2^{2/3} x\right )}{1944\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right ) \left (x^2-3 \sqrt [3]{-3} 2^{2/3} x+6\right )}+\frac {\sqrt [3]{-\frac {1}{3}} \left ((-2)^{2/3} \sqrt [3]{3} x+4\right )}{8748\ 2^{2/3} \left (8+9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right ) \left (x^2+3 (-2)^{2/3} \sqrt [3]{3} x+6\right )}-\frac {2^{2/3} \sqrt [3]{3} x+4}{17496\ 2^{2/3} \sqrt [3]{3} \left (4-3 \sqrt [3]{2} 3^{2/3}\right ) \left (x^2+3\ 2^{2/3} \sqrt [3]{3} x+6\right )}+\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374 \sqrt {3} \left (8-9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374\ 2^{5/6} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^4 \sqrt {4-3 (-3)^{2/3} \sqrt [3]{2}}}-\frac {\tan ^{-1}\left (\frac {2 x+3 (-2)^{2/3} \sqrt [3]{3}}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{4374 \sqrt {3} \left (8+9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {i \tan ^{-1}\left (\frac {2 x+3 (-2)^{2/3} \sqrt [3]{3}}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{1458\ 2^{5/6} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^5 \sqrt {4+3 \sqrt [3]{-2} 3^{2/3}}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (\sqrt [3]{2} x+3 \sqrt [3]{3}\right )}{\sqrt {3 \left (3 \sqrt [3]{2} 3^{2/3}-4\right )}}\right )}{39366\ 2^{5/6} \sqrt [6]{3} \sqrt {3 \sqrt [3]{2} 3^{2/3}-4}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (\sqrt [3]{2} x+3 \sqrt [3]{3}\right )}{\sqrt {3 \left (3 \sqrt [3]{2} 3^{2/3}-4\right )}}\right )}{8748 \sqrt {6} \left (3 \sqrt [3]{2} 3^{2/3}-4\right )^{3/2}} \]
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Rubi [A] time = 1.24, antiderivative size = 682, normalized size of antiderivative = 1.00, number of steps used = 17, number of rules used = 5, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.192, Rules used = {2097, 638, 618, 204, 206} \[ \frac {\sqrt [3]{-\frac {1}{3}} \left (4-\sqrt [3]{-3} 2^{2/3} x\right )}{1944\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right ) \left (x^2-3 \sqrt [3]{-3} 2^{2/3} x+6\right )}+\frac {\sqrt [3]{-\frac {1}{3}} \left ((-2)^{2/3} \sqrt [3]{3} x+4\right )}{8748\ 2^{2/3} \left (8+9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right ) \left (x^2+3 (-2)^{2/3} \sqrt [3]{3} x+6\right )}-\frac {2^{2/3} \sqrt [3]{3} x+4}{17496\ 2^{2/3} \sqrt [3]{3} \left (4-3 \sqrt [3]{2} 3^{2/3}\right ) \left (x^2+3\ 2^{2/3} \sqrt [3]{3} x+6\right )}+\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374 \sqrt {3} \left (8-9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374\ 2^{5/6} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^4 \sqrt {4-3 (-3)^{2/3} \sqrt [3]{2}}}-\frac {\tan ^{-1}\left (\frac {2 x+3 (-2)^{2/3} \sqrt [3]{3}}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{4374 \sqrt {3} \left (8+9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {i \tan ^{-1}\left (\frac {2 x+3 (-2)^{2/3} \sqrt [3]{3}}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{1458\ 2^{5/6} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^5 \sqrt {4+3 \sqrt [3]{-2} 3^{2/3}}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (\sqrt [3]{2} x+3 \sqrt [3]{3}\right )}{\sqrt {3 \left (3 \sqrt [3]{2} 3^{2/3}-4\right )}}\right )}{39366\ 2^{5/6} \sqrt [6]{3} \sqrt {3 \sqrt [3]{2} 3^{2/3}-4}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (\sqrt [3]{2} x+3 \sqrt [3]{3}\right )}{\sqrt {3 \left (3 \sqrt [3]{2} 3^{2/3}-4\right )}}\right )}{8748 \sqrt {6} \left (3 \sqrt [3]{2} 3^{2/3}-4\right )^{3/2}} \]
Antiderivative was successfully verified.
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Rule 204
Rule 206
Rule 618
Rule 638
Rule 2097
Rubi steps
\begin {align*} \int \frac {x^5}{\left (216+108 x^2+324 x^3+18 x^4+x^6\right )^2} \, dx &=1586874322944 \int \left (-\frac {\sqrt [3]{-\frac {1}{3}} x}{1542441841901568\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (-6+3 \sqrt [3]{-3} 2^{2/3} x-x^2\right )^2}-\frac {1}{4627325525704704 \sqrt [3]{2} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (-6+3 \sqrt [3]{-3} 2^{2/3} x-x^2\right )}-\frac {\sqrt [3]{-\frac {1}{3}} x}{1542441841901568\ 2^{2/3} \left (-1+\sqrt [3]{-1}\right )^2 \left (1+\sqrt [3]{-1}\right )^4 \left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )^2}-\frac {i}{4627325525704704 \sqrt [3]{2} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^5 \left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )}+\frac {x}{1542441841901568\ 2^{2/3} \sqrt [3]{3} \left (-1+\sqrt [3]{-1}\right )^2 \left (1+\sqrt [3]{-1}\right )^4 \left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )^2}+\frac {1}{41645929731342336 \sqrt [3]{2} 3^{2/3} \left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )}\right ) \, dx\\ &=-\frac {\sqrt [3]{-\frac {1}{3}} \int \frac {x}{\left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )^2} \, dx}{8748\ 2^{2/3}}+\frac {\int \frac {1}{6+3\ 2^{2/3} \sqrt [3]{3} x+x^2} \, dx}{26244 \sqrt [3]{2} 3^{2/3}}+\frac {\int \frac {x}{\left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )^2} \, dx}{8748\ 2^{2/3} \sqrt [3]{3}}-\frac {i \int \frac {1}{6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2} \, dx}{2916 \sqrt [3]{2} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^5}-\frac {\sqrt [3]{-\frac {1}{3}} \int \frac {x}{\left (-6+3 \sqrt [3]{-3} 2^{2/3} x-x^2\right )^2} \, dx}{972\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4}-\frac {\int \frac {1}{-6+3 \sqrt [3]{-3} 2^{2/3} x-x^2} \, dx}{2916 \sqrt [3]{2} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^4}\\ &=\frac {\sqrt [3]{-\frac {1}{3}} \left (4-\sqrt [3]{-3} 2^{2/3} x\right )}{1944\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right ) \left (6-3 \sqrt [3]{-3} 2^{2/3} x+x^2\right )}+\frac {\sqrt [3]{-\frac {1}{3}} \left (4+(-2)^{2/3} \sqrt [3]{3} x\right )}{17496\ 2^{2/3} \left (4+3 \sqrt [3]{-2} 3^{2/3}\right ) \left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {4+2^{2/3} \sqrt [3]{3} x}{17496\ 2^{2/3} \sqrt [3]{3} \left (4-3 \sqrt [3]{2} 3^{2/3}\right ) \left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {1}{-6 \left (4-3 \sqrt [3]{2} 3^{2/3}\right )-x^2} \, dx,x,3\ 2^{2/3} \sqrt [3]{3}+2 x\right )}{13122 \sqrt [3]{2} 3^{2/3}}+\frac {i \operatorname {Subst}\left (\int \frac {1}{-6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )-x^2} \, dx,x,3 (-2)^{2/3} \sqrt [3]{3}+2 x\right )}{1458 \sqrt [3]{2} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^5}+\frac {\operatorname {Subst}\left (\int \frac {1}{-6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )-x^2} \, dx,x,3 \sqrt [3]{-3} 2^{2/3}-2 x\right )}{1458 \sqrt [3]{2} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^4}-\frac {\int \frac {1}{6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2} \, dx}{17496 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}-\frac {\int \frac {1}{6+3\ 2^{2/3} \sqrt [3]{3} x+x^2} \, dx}{17496 \left (4-3 \sqrt [3]{2} 3^{2/3}\right )}+\frac {\int \frac {1}{-6+3 \sqrt [3]{-3} 2^{2/3} x-x^2} \, dx}{8748 \left (8-9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )}\\ &=\frac {\sqrt [3]{-\frac {1}{3}} \left (4-\sqrt [3]{-3} 2^{2/3} x\right )}{1944\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right ) \left (6-3 \sqrt [3]{-3} 2^{2/3} x+x^2\right )}+\frac {\sqrt [3]{-\frac {1}{3}} \left (4+(-2)^{2/3} \sqrt [3]{3} x\right )}{17496\ 2^{2/3} \left (4+3 \sqrt [3]{-2} 3^{2/3}\right ) \left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {4+2^{2/3} \sqrt [3]{3} x}{17496\ 2^{2/3} \sqrt [3]{3} \left (4-3 \sqrt [3]{2} 3^{2/3}\right ) \left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374\ 2^{5/6} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^4 \sqrt {4-3 (-3)^{2/3} \sqrt [3]{2}}}-\frac {i \tan ^{-1}\left (\frac {3 (-2)^{2/3} \sqrt [3]{3}+2 x}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{1458\ 2^{5/6} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^5 \sqrt {4+3 \sqrt [3]{-2} 3^{2/3}}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (3 \sqrt [3]{3}+\sqrt [3]{2} x\right )}{\sqrt {3 \left (-4+3 \sqrt [3]{2} 3^{2/3}\right )}}\right )}{39366\ 2^{5/6} \sqrt [6]{3} \sqrt {-4+3 \sqrt [3]{2} 3^{2/3}}}+\frac {\operatorname {Subst}\left (\int \frac {1}{-6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )-x^2} \, dx,x,3 (-2)^{2/3} \sqrt [3]{3}+2 x\right )}{8748 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}+\frac {\operatorname {Subst}\left (\int \frac {1}{-6 \left (4-3 \sqrt [3]{2} 3^{2/3}\right )-x^2} \, dx,x,3\ 2^{2/3} \sqrt [3]{3}+2 x\right )}{8748 \left (4-3 \sqrt [3]{2} 3^{2/3}\right )}-\frac {\operatorname {Subst}\left (\int \frac {1}{-6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )-x^2} \, dx,x,3 \sqrt [3]{-3} 2^{2/3}-2 x\right )}{4374 \left (8-9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )}\\ &=\frac {\sqrt [3]{-\frac {1}{3}} \left (4-\sqrt [3]{-3} 2^{2/3} x\right )}{1944\ 2^{2/3} \left (1+\sqrt [3]{-1}\right )^4 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right ) \left (6-3 \sqrt [3]{-3} 2^{2/3} x+x^2\right )}+\frac {\sqrt [3]{-\frac {1}{3}} \left (4+(-2)^{2/3} \sqrt [3]{3} x\right )}{17496\ 2^{2/3} \left (4+3 \sqrt [3]{-2} 3^{2/3}\right ) \left (6+3 (-2)^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {4+2^{2/3} \sqrt [3]{3} x}{17496\ 2^{2/3} \sqrt [3]{3} \left (4-3 \sqrt [3]{2} 3^{2/3}\right ) \left (6+3\ 2^{2/3} \sqrt [3]{3} x+x^2\right )}-\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374\ 2^{5/6} \sqrt [6]{3} \left (1+\sqrt [3]{-1}\right )^4 \sqrt {4-3 (-3)^{2/3} \sqrt [3]{2}}}+\frac {\tan ^{-1}\left (\frac {3 \sqrt [3]{-3} 2^{2/3}-2 x}{\sqrt {6 \left (4-3 (-3)^{2/3} \sqrt [3]{2}\right )}}\right )}{4374 \sqrt {3} \left (8-9 i \sqrt [3]{2} \sqrt [6]{3}+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {\tan ^{-1}\left (\frac {3 (-2)^{2/3} \sqrt [3]{3}+2 x}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{8748 \sqrt {6} \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )^{3/2}}-\frac {i \tan ^{-1}\left (\frac {3 (-2)^{2/3} \sqrt [3]{3}+2 x}{\sqrt {6 \left (4+3 \sqrt [3]{-2} 3^{2/3}\right )}}\right )}{1458\ 2^{5/6} 3^{2/3} \left (1+\sqrt [3]{-1}\right )^5 \sqrt {4+3 \sqrt [3]{-2} 3^{2/3}}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (3 \sqrt [3]{3}+\sqrt [3]{2} x\right )}{\sqrt {3 \left (-4+3 \sqrt [3]{2} 3^{2/3}\right )}}\right )}{8748 \sqrt {6} \left (-4+3 \sqrt [3]{2} 3^{2/3}\right )^{3/2}}-\frac {\tanh ^{-1}\left (\frac {\sqrt [6]{2} \left (3 \sqrt [3]{3}+\sqrt [3]{2} x\right )}{\sqrt {3 \left (-4+3 \sqrt [3]{2} 3^{2/3}\right )}}\right )}{39366\ 2^{5/6} \sqrt [6]{3} \sqrt {-4+3 \sqrt [3]{2} 3^{2/3}}}\\ \end {align*}
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Mathematica [C] time = 0.03, size = 167, normalized size = 0.24 \[ \frac {\text {RootSum}\left [\text {$\#$1}^6+18 \text {$\#$1}^4+324 \text {$\#$1}^3+108 \text {$\#$1}^2+216\& ,\frac {4 \text {$\#$1}^4 \log (x-\text {$\#$1})-54 \text {$\#$1}^3 \log (x-\text {$\#$1})+2043 \text {$\#$1}^2 \log (x-\text {$\#$1})-324 \text {$\#$1} \log (x-\text {$\#$1})+144 \log (x-\text {$\#$1})}{\text {$\#$1}^5+12 \text {$\#$1}^3+162 \text {$\#$1}^2+36 \text {$\#$1}}\& \right ]}{3691656}+\frac {4 x^5-27 x^4+729 x^3+648 x^2-144 x+972}{615276 \left (x^6+18 x^4+324 x^3+108 x^2+216\right )} \]
Warning: Unable to verify antiderivative.
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fricas [B] time = 2.97, size = 1445, normalized size = 2.12 \[ \text {result too large to display} \]
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 \[ \int \frac {x^{5}}{{\left (x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.01, size = 122, normalized size = 0.18 \[ \frac {\left (4 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{4}-54 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{3}+2043 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{2}-324 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )+144\right ) \ln \left (-\RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )+x \right )}{3691656 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{5}+44299872 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{3}+598048272 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )^{2}+132899616 \RootOf \left (\textit {\_Z}^{6}+18 \textit {\_Z}^{4}+324 \textit {\_Z}^{3}+108 \textit {\_Z}^{2}+216\right )}+\frac {\frac {1}{153819} x^{5}-\frac {1}{22788} x^{4}+\frac {1}{844} x^{3}+\frac {2}{1899} x^{2}-\frac {4}{17091} x +\frac {1}{633}}{x^{6}+18 x^{4}+324 x^{3}+108 x^{2}+216} \]
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 \[ \frac {4 \, x^{5} - 27 \, x^{4} + 729 \, x^{3} + 648 \, x^{2} - 144 \, x + 972}{615276 \, {\left (x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216\right )}} + \frac {1}{615276} \, \int \frac {4 \, x^{4} - 54 \, x^{3} + 2043 \, x^{2} - 324 \, x + 144}{x^{6} + 18 \, x^{4} + 324 \, x^{3} + 108 \, x^{2} + 216}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 299, normalized size = 0.44 \[ \left (\sum _{k=1}^6\ln \left (-\frac {4477969\,\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}{189282278088}+\frac {6305\,x}{4967524106141472}-\frac {\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )\,x\,16340881}{5110621508376}-\frac {{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^2\,x\,43348696}{10818603}-\frac {{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^3\,x\,65333687616}{44521}-\frac {{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^4\,x\,40024496812032}{211}-{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^5\,x\,6940988288557056+\frac {5943884\,{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^2}{400689}+\frac {224442467136\,{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^3}{44521}-\frac {137087493272064\,{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^4}{211}-168897381688221696\,{\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )}^5-\frac {13082875}{178830867821092992}\right )\,\mathrm {root}\left (z^6-\frac {183899\,z^4}{3834101824950528}+\frac {6209\,z^2}{14083883651774823903461376}-\frac {39753025}{27493895104978847349012449000830556700672},z,k\right )\right )+\frac {\frac {x^5}{153819}-\frac {x^4}{22788}+\frac {x^3}{844}+\frac {2\,x^2}{1899}-\frac {4\,x}{17091}+\frac {1}{633}}{x^6+18\,x^4+324\,x^3+108\,x^2+216} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 104, normalized size = 0.15 \[ \operatorname {RootSum} {\left (27493895104978847349012449000830556700672 t^{6} - 1318718189226950088862983192576 t^{4} + 12120917704776776448 t^{2} - 39753025, \left (t \mapsto t \log {\left (\frac {947842259001288723909832054550209950242045952 t^{5}}{61864539719962655} - \frac {243458646817775607639654889480814592 t^{4}}{9811980923071} - \frac {41682556475067500431787310779667456 t^{3}}{61864539719962655} + \frac {12026877442664328616462272 t^{2}}{9811980923071} + \frac {216142618488859793668428 t}{61864539719962655} + x - \frac {308574300024117}{39247923692284} \right )} \right )\right )} + \frac {4 x^{5} - 27 x^{4} + 729 x^{3} + 648 x^{2} - 144 x + 972}{615276 x^{6} + 11074968 x^{4} + 199349424 x^{3} + 66449808 x^{2} + 132899616} \]
Verification of antiderivative is not currently implemented for this CAS.
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