Optimal. Leaf size=25 \[ \left (\frac {x^2}{e^3+x}\right )^{\left (5+\frac {x}{6}\right )^2+2 x} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A] time = 5.15, size = 31, normalized size = 1.24 \begin {gather*} \frac {x^{50} \left (\frac {x^2}{e^3+x}\right )^{\frac {1}{36} x (132+x)}}{\left (e^3+x\right )^{25}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 21, normalized size = 0.84 \begin {gather*} \left (\frac {x^{2}}{x + e^{3}}\right )^{\frac {1}{36} \, x^{2} + \frac {11}{3} \, x + 25} \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} + 132 \, x^{2} + 2 \, {\left (x^{2} + 132 \, x + 900\right )} e^{3} + 2 \, {\left (x^{3} + 66 \, x^{2} + {\left (x^{2} + 66 \, x\right )} e^{3}\right )} \log \left (\frac {x^{2}}{x + e^{3}}\right ) + 900 \, x\right )} \left (\frac {x^{2}}{x + e^{3}}\right )^{\frac {1}{36} \, x^{2} + \frac {11}{3} \, x + 25}}{36 \, {\left (x^{2} + x e^{3}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 22, normalized size = 0.88
method | result | size |
risch | \(\left (\frac {x^{2}}{{\mathrm e}^{3}+x}\right )^{\frac {1}{36} x^{2}+\frac {11}{3} x +25}\) | \(22\) |
norman | \({\mathrm e}^{\frac {\left (x^{2}+132 x +900\right ) \ln \left (\frac {x^{2}}{{\mathrm e}^{3}+x}\right )}{36}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.65, size = 210, normalized size = 8.40 \begin {gather*} \frac {x^{50} e^{\left (-\frac {1}{36} \, x^{2} \log \left (x + e^{3}\right ) + \frac {1}{18} \, x^{2} \log \relax (x) - \frac {11}{3} \, x \log \left (x + e^{3}\right ) + \frac {22}{3} \, x \log \relax (x)\right )}}{x^{25} + 25 \, x^{24} e^{3} + 300 \, x^{23} e^{6} + 2300 \, x^{22} e^{9} + 12650 \, x^{21} e^{12} + 53130 \, x^{20} e^{15} + 177100 \, x^{19} e^{18} + 480700 \, x^{18} e^{21} + 1081575 \, x^{17} e^{24} + 2042975 \, x^{16} e^{27} + 3268760 \, x^{15} e^{30} + 4457400 \, x^{14} e^{33} + 5200300 \, x^{13} e^{36} + 5200300 \, x^{12} e^{39} + 4457400 \, x^{11} e^{42} + 3268760 \, x^{10} e^{45} + 2042975 \, x^{9} e^{48} + 1081575 \, x^{8} e^{51} + 480700 \, x^{7} e^{54} + 177100 \, x^{6} e^{57} + 53130 \, x^{5} e^{60} + 12650 \, x^{4} e^{63} + 2300 \, x^{3} e^{66} + 300 \, x^{2} e^{69} + 25 \, x e^{72} + e^{75}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.06, size = 217, normalized size = 8.68 \begin {gather*} \frac {x^{50}\,{\mathrm {e}}^{\frac {11\,x\,\ln \left (\frac {1}{x+{\mathrm {e}}^3}\right )}{3}}\,{\left (\frac {1}{x+{\mathrm {e}}^3}\right )}^{\frac {x^2}{36}}\,{\left (x^2\right )}^{\frac {11\,x}{3}}\,{\left (x^2\right )}^{\frac {x^2}{36}}}{x^{25}+25\,{\mathrm {e}}^3\,x^{24}+300\,{\mathrm {e}}^6\,x^{23}+2300\,{\mathrm {e}}^9\,x^{22}+12650\,{\mathrm {e}}^{12}\,x^{21}+53130\,{\mathrm {e}}^{15}\,x^{20}+177100\,{\mathrm {e}}^{18}\,x^{19}+480700\,{\mathrm {e}}^{21}\,x^{18}+1081575\,{\mathrm {e}}^{24}\,x^{17}+2042975\,{\mathrm {e}}^{27}\,x^{16}+3268760\,{\mathrm {e}}^{30}\,x^{15}+4457400\,{\mathrm {e}}^{33}\,x^{14}+5200300\,{\mathrm {e}}^{36}\,x^{13}+5200300\,{\mathrm {e}}^{39}\,x^{12}+4457400\,{\mathrm {e}}^{42}\,x^{11}+3268760\,{\mathrm {e}}^{45}\,x^{10}+2042975\,{\mathrm {e}}^{48}\,x^9+1081575\,{\mathrm {e}}^{51}\,x^8+480700\,{\mathrm {e}}^{54}\,x^7+177100\,{\mathrm {e}}^{57}\,x^6+53130\,{\mathrm {e}}^{60}\,x^5+12650\,{\mathrm {e}}^{63}\,x^4+2300\,{\mathrm {e}}^{66}\,x^3+300\,{\mathrm {e}}^{69}\,x^2+25\,{\mathrm {e}}^{72}\,x+{\mathrm {e}}^{75}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.86, size = 22, normalized size = 0.88 \begin {gather*} e^{\left (\frac {x^{2}}{36} + \frac {11 x}{3} + 25\right ) \log {\left (\frac {x^{2}}{x + e^{3}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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