Optimal. Leaf size=27 \[ \left (10+\frac {\sqrt [3]{e}}{-1+x+\left (6+\frac {\log \left (x^2\right )}{x}\right )^2}\right )^2 \]
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Rubi [F] time = 3.21, 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 {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \sqrt [3]{e} x \left (-x^2 \left (\sqrt [3]{e}+10 (35+x)\right )-120 x \log \left (x^2\right )-10 \log ^2\left (x^2\right )\right ) \left (x \left (24+x^2\right )+(4-12 x) \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (2 \sqrt [3]{e}\right ) \int \frac {x \left (-x^2 \left (\sqrt [3]{e}+10 (35+x)\right )-120 x \log \left (x^2\right )-10 \log ^2\left (x^2\right )\right ) \left (x \left (24+x^2\right )+(4-12 x) \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (2 \sqrt [3]{e}\right ) \int \left (-\frac {\sqrt [3]{e} x^3 \left (24 x+70 x^2+3 x^3+4 \log \left (x^2\right )+12 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {2 x \left (-120 x-350 \left (1-\frac {\sqrt [3]{e}}{350}\right ) x^2-15 x^3-20 \log \left (x^2\right )-60 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}+\frac {20 x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )}\right ) \, dx\\ &=\left (4 \sqrt [3]{e}\right ) \int \frac {x \left (-120 x-350 \left (1-\frac {\sqrt [3]{e}}{350}\right ) x^2-15 x^3-20 \log \left (x^2\right )-60 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx+\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (2 e^{2/3}\right ) \int \frac {x^3 \left (24 x+70 x^2+3 x^3+4 \log \left (x^2\right )+12 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (4 \sqrt [3]{e}\right ) \int \left (-\frac {120 x^2}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}+\frac {\left (-350+\sqrt [3]{e}\right ) x^3}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {15 x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {20 x \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {60 x^2 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}\right ) \, dx+\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (2 e^{2/3}\right ) \int \left (\frac {24 x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {70 x^5}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {3 x^6}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {4 x^3 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {12 x^4 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}\right ) \, dx\\ &=\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (60 \sqrt [3]{e}\right ) \int \frac {x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (80 \sqrt [3]{e}\right ) \int \frac {x \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (240 \sqrt [3]{e}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (480 \sqrt [3]{e}\right ) \int \frac {x^2}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (4 \left (350-\sqrt [3]{e}\right ) \sqrt [3]{e}\right ) \int \frac {x^3}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (6 e^{2/3}\right ) \int \frac {x^6}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (8 e^{2/3}\right ) \int \frac {x^3 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (24 e^{2/3}\right ) \int \frac {x^4 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (48 e^{2/3}\right ) \int \frac {x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (140 e^{2/3}\right ) \int \frac {x^5}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.09, size = 63, normalized size = 2.33 \begin {gather*} \frac {\sqrt [3]{e} x^2 \left (x^2 \left (\sqrt [3]{e}+20 (35+x)\right )+240 x \log \left (x^2\right )+20 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.87, size = 108, normalized size = 4.00 \begin {gather*} \frac {x^{4} e^{\frac {2}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2} + 20 \, {\left (x^{5} + 35 \, x^{4}\right )} e^{\frac {1}{3}}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4} + 2 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 24 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.72, size = 117, normalized size = 4.33 \begin {gather*} \frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 \, x^{4} e^{\frac {1}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2}}{x^{6} + 70 \, x^{5} + 24 \, x^{4} \log \left (x^{2}\right ) + 2 \, x^{3} \log \left (x^{2}\right )^{2} + 1225 \, x^{4} + 840 \, x^{3} \log \left (x^{2}\right ) + 214 \, x^{2} \log \left (x^{2}\right )^{2} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 63, normalized size = 2.33
method | result | size |
risch | \(\frac {\left (x^{2} {\mathrm e}^{\frac {1}{3}}+20 x^{3}+700 x^{2}+240 x \ln \left (x^{2}\right )+20 \ln \left (x^{2}\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {1}{3}}}{\left (x^{3}+\ln \left (x^{2}\right )^{2}+12 x \ln \left (x^{2}\right )+35 x^{2}\right )^{2}}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 5.43, size = 97, normalized size = 3.59 \begin {gather*} \frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} {\left (e^{\frac {2}{3}} + 700 \, e^{\frac {1}{3}}\right )} + 480 \, x^{3} e^{\frac {1}{3}} \log \relax (x) + 80 \, x^{2} e^{\frac {1}{3}} \log \relax (x)^{2}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 192 \, x \log \relax (x)^{3} + 16 \, \log \relax (x)^{4} + 8 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \relax (x)^{2} + 48 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \relax (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 = -0.04 \begin {gather*} \int -\frac {-40\,x\,{\mathrm {e}}^{1/3}\,{\ln \left (x^2\right )}^4+{\mathrm {e}}^{1/3}\,\left (80\,x-720\,x^2\right )\,{\ln \left (x^2\right )}^3+\left (-4\,x^3\,{\mathrm {e}}^{2/3}-{\mathrm {e}}^{1/3}\,\left (20\,x^4+4280\,x^3-1440\,x^2\right )\right )\,{\ln \left (x^2\right )}^2+\left ({\mathrm {e}}^{2/3}\,\left (8\,x^3-24\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (8560\,x^3-8320\,x^4\right )\right )\,\ln \left (x^2\right )+{\mathrm {e}}^{2/3}\,\left (2\,x^6+48\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (20\,x^7+700\,x^6+480\,x^5+16800\,x^4\right )}{{\ln \left (x^2\right )}^2\,\left (3\,x^6+642\,x^5+18795\,x^4\right )+36\,x\,{\ln \left (x^2\right )}^5+{\ln \left (x^2\right )}^6+\ln \left (x^2\right )\,\left (36\,x^7+2520\,x^6+44100\,x^5\right )+{\ln \left (x^2\right )}^4\,\left (3\,x^3+537\,x^2\right )+{\ln \left (x^2\right )}^3\,\left (72\,x^4+4248\,x^3\right )+42875\,x^6+3675\,x^7+105\,x^8+x^9} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.31, size = 122, normalized size = 4.52 \begin {gather*} \frac {20 x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 x^{4} e^{\frac {1}{3}} + 240 x^{3} e^{\frac {1}{3}} \log {\left (x^{2} \right )} + 20 x^{2} e^{\frac {1}{3}} \log {\left (x^{2} \right )}^{2}}{x^{6} + 70 x^{5} + 1225 x^{4} + 24 x \log {\left (x^{2} \right )}^{3} + \left (2 x^{3} + 214 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (24 x^{4} + 840 x^{3}\right ) \log {\left (x^{2} \right )} + \log {\left (x^{2} \right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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