Optimal. Leaf size=242 \[ \frac {5 x^3}{3}-\frac {21}{512} \sqrt {22721 \sqrt {3}-34271} \log \left (x^2-\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+\frac {21}{512} \sqrt {22721 \sqrt {3}-34271} \log \left (x^2+\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )-\frac {\left (835 x^2+1468\right ) x}{64 \left (x^4+2 x^2+3\right )}+\frac {25 \left (5 x^2+3\right ) x}{16 \left (x^4+2 x^2+3\right )^2}-27 x-\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {\sqrt {2 \left (\sqrt {3}-1\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )+\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {2 x+\sqrt {2 \left (\sqrt {3}-1\right )}}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right ) \]
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Rubi [A] time = 0.31, antiderivative size = 242, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 8, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.258, Rules used = {1668, 1678, 1676, 1169, 634, 618, 204, 628} \[ \frac {5 x^3}{3}-\frac {\left (835 x^2+1468\right ) x}{64 \left (x^4+2 x^2+3\right )}+\frac {25 \left (5 x^2+3\right ) x}{16 \left (x^4+2 x^2+3\right )^2}-\frac {21}{512} \sqrt {22721 \sqrt {3}-34271} \log \left (x^2-\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+\frac {21}{512} \sqrt {22721 \sqrt {3}-34271} \log \left (x^2+\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )-27 x-\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {\sqrt {2 \left (\sqrt {3}-1\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )+\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {2 x+\sqrt {2 \left (\sqrt {3}-1\right )}}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right ) \]
Antiderivative was successfully verified.
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Rule 204
Rule 618
Rule 628
Rule 634
Rule 1169
Rule 1668
Rule 1676
Rule 1678
Rubi steps
\begin {align*} \int \frac {x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx &=\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}+\frac {1}{96} \int \frac {-450-1050 x^2+2400 x^4-672 x^8+480 x^{10}}{\left (3+2 x^2+x^4\right )^2} \, dx\\ &=\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}+\frac {\int \frac {98496+27432 x^2-78336 x^4+23040 x^6}{3+2 x^2+x^4} \, dx}{4608}\\ &=\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}+\frac {\int \left (-124416+23040 x^2+\frac {1512 \left (312+137 x^2\right )}{3+2 x^2+x^4}\right ) \, dx}{4608}\\ &=-27 x+\frac {5 x^3}{3}+\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}+\frac {21}{64} \int \frac {312+137 x^2}{3+2 x^2+x^4} \, dx\\ &=-27 x+\frac {5 x^3}{3}+\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}+\frac {1}{256} \left (7 \sqrt {3 \left (1+\sqrt {3}\right )}\right ) \int \frac {312 \sqrt {2 \left (-1+\sqrt {3}\right )}-\left (312-137 \sqrt {3}\right ) x}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx+\frac {1}{256} \left (7 \sqrt {3 \left (1+\sqrt {3}\right )}\right ) \int \frac {312 \sqrt {2 \left (-1+\sqrt {3}\right )}+\left (312-137 \sqrt {3}\right ) x}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx\\ &=-27 x+\frac {5 x^3}{3}+\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}-\frac {1}{512} \left (21 \sqrt {-34271+22721 \sqrt {3}}\right ) \int \frac {-\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx+\frac {1}{512} \left (21 \sqrt {-34271+22721 \sqrt {3}}\right ) \int \frac {\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx+\frac {1}{256} \left (21 \sqrt {51217+28496 \sqrt {3}}\right ) \int \frac {1}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx+\frac {1}{256} \left (21 \sqrt {51217+28496 \sqrt {3}}\right ) \int \frac {1}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx\\ &=-27 x+\frac {5 x^3}{3}+\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}-\frac {21}{512} \sqrt {-34271+22721 \sqrt {3}} \log \left (\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )+\frac {21}{512} \sqrt {-34271+22721 \sqrt {3}} \log \left (\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )-\frac {1}{128} \left (21 \sqrt {51217+28496 \sqrt {3}}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (1+\sqrt {3}\right )-x^2} \, dx,x,-\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x\right )-\frac {1}{128} \left (21 \sqrt {51217+28496 \sqrt {3}}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (1+\sqrt {3}\right )-x^2} \, dx,x,\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x\right )\\ &=-27 x+\frac {5 x^3}{3}+\frac {25 x \left (3+5 x^2\right )}{16 \left (3+2 x^2+x^4\right )^2}-\frac {x \left (1468+835 x^2\right )}{64 \left (3+2 x^2+x^4\right )}-\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {\sqrt {2 \left (-1+\sqrt {3}\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )+\frac {21}{256} \sqrt {34271+22721 \sqrt {3}} \tan ^{-1}\left (\frac {\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )-\frac {21}{512} \sqrt {-34271+22721 \sqrt {3}} \log \left (\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )+\frac {21}{512} \sqrt {-34271+22721 \sqrt {3}} \log \left (\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )\\ \end {align*}
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Mathematica [C] time = 0.20, size = 155, normalized size = 0.64 \[ \frac {5 x^3}{3}-\frac {\left (835 x^2+1468\right ) x}{64 \left (x^4+2 x^2+3\right )}+\frac {25 \left (5 x^2+3\right ) x}{16 \left (x^4+2 x^2+3\right )^2}-27 x+\frac {21 \left (137 \sqrt {2}-175 i\right ) \tan ^{-1}\left (\frac {x}{\sqrt {1-i \sqrt {2}}}\right )}{128 \sqrt {2-2 i \sqrt {2}}}+\frac {21 \left (137 \sqrt {2}+175 i\right ) \tan ^{-1}\left (\frac {x}{\sqrt {1+i \sqrt {2}}}\right )}{128 \sqrt {2+2 i \sqrt {2}}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.84, size = 557, normalized size = 2.30 \[ \frac {1591298862080 \, x^{11} - 19413846117376 \, x^{9} - 99660064046704 \, x^{7} - 285508852710816 \, x^{5} - 2298072 \cdot 1548731523^{\frac {1}{4}} \sqrt {3} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} \arctan \left (\frac {1}{19753021371716480527209} \cdot 1548731523^{\frac {3}{4}} \sqrt {932401677} \sqrt {932401677 \, x^{2} + 1548731523^{\frac {1}{4}} {\left (137 \, \sqrt {3} \sqrt {2} x - 312 \, \sqrt {2} x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} + 932401677 \, \sqrt {3}} \sqrt {778671391 \, \sqrt {3} + 1548731523} {\left (104 \, \sqrt {3} - 137\right )} - \frac {1}{21185098503117} \cdot 1548731523^{\frac {3}{4}} {\left (104 \, \sqrt {3} x - 137 \, x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} + \frac {1}{2} \, \sqrt {3} \sqrt {2} - \frac {1}{2} \, \sqrt {2}\right ) - 2298072 \cdot 1548731523^{\frac {1}{4}} \sqrt {3} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} \arctan \left (\frac {1}{19753021371716480527209} \cdot 1548731523^{\frac {3}{4}} \sqrt {932401677} \sqrt {932401677 \, x^{2} - 1548731523^{\frac {1}{4}} {\left (137 \, \sqrt {3} \sqrt {2} x - 312 \, \sqrt {2} x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} + 932401677 \, \sqrt {3}} \sqrt {778671391 \, \sqrt {3} + 1548731523} {\left (104 \, \sqrt {3} - 137\right )} - \frac {1}{21185098503117} \cdot 1548731523^{\frac {3}{4}} {\left (104 \, \sqrt {3} x - 137 \, x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} - \frac {1}{2} \, \sqrt {3} \sqrt {2} + \frac {1}{2} \, \sqrt {2}\right ) - 368738756006544 \, x^{3} + 21 \cdot 1548731523^{\frac {1}{4}} {\left (34271 \, \sqrt {3} \sqrt {2} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )} - 68163 \, \sqrt {2} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )}\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} \log \left (932401677 \, x^{2} + 1548731523^{\frac {1}{4}} {\left (137 \, \sqrt {3} \sqrt {2} x - 312 \, \sqrt {2} x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} + 932401677 \, \sqrt {3}\right ) - 21 \cdot 1548731523^{\frac {1}{4}} {\left (34271 \, \sqrt {3} \sqrt {2} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )} - 68163 \, \sqrt {2} {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )}\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} \log \left (932401677 \, x^{2} - 1548731523^{\frac {1}{4}} {\left (137 \, \sqrt {3} \sqrt {2} x - 312 \, \sqrt {2} x\right )} \sqrt {778671391 \, \sqrt {3} + 1548731523} + 932401677 \, \sqrt {3}\right ) - 293236597809792 \, x}{954779317248 \, {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.59, size = 585, normalized size = 2.42 \[ \frac {5}{3} \, x^{3} - \frac {7}{55296} \, \sqrt {2} {\left (137 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 2466 \cdot 3^{\frac {3}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 2466 \cdot 3^{\frac {3}{4}} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} + 137 \cdot 3^{\frac {3}{4}} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} + 11232 \cdot 3^{\frac {1}{4}} \sqrt {-6 \, \sqrt {3} + 18}\right )} \arctan \left (\frac {3^{\frac {3}{4}} {\left (x + 3^{\frac {1}{4}} \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}\right )}}{3 \, \sqrt {\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}}\right ) - \frac {7}{55296} \, \sqrt {2} {\left (137 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 2466 \cdot 3^{\frac {3}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 2466 \cdot 3^{\frac {3}{4}} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} + 137 \cdot 3^{\frac {3}{4}} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} + 11232 \cdot 3^{\frac {1}{4}} \sqrt {-6 \, \sqrt {3} + 18}\right )} \arctan \left (\frac {3^{\frac {3}{4}} {\left (x - 3^{\frac {1}{4}} \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}\right )}}{3 \, \sqrt {\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}}\right ) - \frac {7}{110592} \, \sqrt {2} {\left (2466 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} - 137 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 137 \cdot 3^{\frac {3}{4}} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 2466 \cdot 3^{\frac {3}{4}} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {-6 \, \sqrt {3} + 18} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {6 \, \sqrt {3} + 18}\right )} \log \left (x^{2} + 2 \cdot 3^{\frac {1}{4}} x \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}} + \sqrt {3}\right ) + \frac {7}{110592} \, \sqrt {2} {\left (2466 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} - 137 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 137 \cdot 3^{\frac {3}{4}} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 2466 \cdot 3^{\frac {3}{4}} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {-6 \, \sqrt {3} + 18} - 11232 \cdot 3^{\frac {1}{4}} \sqrt {6 \, \sqrt {3} + 18}\right )} \log \left (x^{2} - 2 \cdot 3^{\frac {1}{4}} x \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}} + \sqrt {3}\right ) - 27 \, x - \frac {835 \, x^{7} + 3138 \, x^{5} + 4941 \, x^{3} + 4104 \, x}{64 \, {\left (x^{4} + 2 \, x^{2} + 3\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.03, size = 426, normalized size = 1.76 \[ \frac {5 x^{3}}{3}-27 x +\frac {693 \left (-2+2 \sqrt {3}\right ) \sqrt {3}\, \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{512 \sqrt {2+2 \sqrt {3}}}-\frac {3675 \left (-2+2 \sqrt {3}\right ) \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{512 \sqrt {2+2 \sqrt {3}}}+\frac {273 \sqrt {3}\, \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{8 \sqrt {2+2 \sqrt {3}}}+\frac {693 \left (-2+2 \sqrt {3}\right ) \sqrt {3}\, \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{512 \sqrt {2+2 \sqrt {3}}}-\frac {3675 \left (-2+2 \sqrt {3}\right ) \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{512 \sqrt {2+2 \sqrt {3}}}+\frac {273 \sqrt {3}\, \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{8 \sqrt {2+2 \sqrt {3}}}+\frac {693 \sqrt {-2+2 \sqrt {3}}\, \sqrt {3}\, \ln \left (x^{2}-\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{1024}-\frac {3675 \sqrt {-2+2 \sqrt {3}}\, \ln \left (x^{2}-\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{1024}-\frac {693 \sqrt {-2+2 \sqrt {3}}\, \sqrt {3}\, \ln \left (x^{2}+\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{1024}+\frac {3675 \sqrt {-2+2 \sqrt {3}}\, \ln \left (x^{2}+\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{1024}+\frac {-\frac {835}{64} x^{7}-\frac {1569}{32} x^{5}-\frac {4941}{64} x^{3}-\frac {513}{8} x}{\left (x^{4}+2 x^{2}+3\right )^{2}} \]
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 \[ \frac {5}{3} \, x^{3} - 27 \, x - \frac {835 \, x^{7} + 3138 \, x^{5} + 4941 \, x^{3} + 4104 \, x}{64 \, {\left (x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right )}} + \frac {21}{64} \, \int \frac {137 \, x^{2} + 312}{x^{4} + 2 \, x^{2} + 3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 182, normalized size = 0.75 \[ \frac {5\,x^3}{3}-\frac {\frac {835\,x^7}{64}+\frac {1569\,x^5}{32}+\frac {4941\,x^3}{64}+\frac {513\,x}{8}}{x^8+4\,x^6+10\,x^4+12\,x^2+9}-27\,x+\frac {\mathrm {atan}\left (\frac {x\,\sqrt {-68542-\sqrt {2}\,27358{}\mathrm {i}}\,126681219{}\mathrm {i}}{131072\,\left (\frac {12541440681}{131072}+\frac {\sqrt {2}\,4940567541{}\mathrm {i}}{16384}\right )}-\frac {126681219\,\sqrt {2}\,x\,\sqrt {-68542-\sqrt {2}\,27358{}\mathrm {i}}}{262144\,\left (\frac {12541440681}{131072}+\frac {\sqrt {2}\,4940567541{}\mathrm {i}}{16384}\right )}\right )\,\sqrt {-68542-\sqrt {2}\,27358{}\mathrm {i}}\,21{}\mathrm {i}}{256}-\frac {\mathrm {atan}\left (\frac {x\,\sqrt {-68542+\sqrt {2}\,27358{}\mathrm {i}}\,126681219{}\mathrm {i}}{131072\,\left (-\frac {12541440681}{131072}+\frac {\sqrt {2}\,4940567541{}\mathrm {i}}{16384}\right )}+\frac {126681219\,\sqrt {2}\,x\,\sqrt {-68542+\sqrt {2}\,27358{}\mathrm {i}}}{262144\,\left (-\frac {12541440681}{131072}+\frac {\sqrt {2}\,4940567541{}\mathrm {i}}{16384}\right )}\right )\,\sqrt {-68542+\sqrt {2}\,27358{}\mathrm {i}}\,21{}\mathrm {i}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.68, size = 82, normalized size = 0.34 \[ \frac {5 x^{3}}{3} - 27 x + \frac {- 835 x^{7} - 3138 x^{5} - 4941 x^{3} - 4104 x}{64 x^{8} + 256 x^{6} + 640 x^{4} + 768 x^{2} + 576} + 21 \operatorname {RootSum} {\left (17179869184 t^{4} + 8983937024 t^{2} + 1548731523, \left (t \mapsto t \log {\left (- \frac {1107296256 t^{3}}{310800559} + \frac {438857984 t}{310800559} + x \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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