Optimal. Leaf size=29 \[ \log ^4\left (e^{-x+\frac {-1+x+2 \log (5)}{2 x}}-16 x^4\right ) \]
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Rubi [A] time = 0.54, antiderivative size = 34, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 1, integrand size = 103, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6686} \begin {gather*} \log ^4\left (5^{\frac {1}{x}} e^{-\frac {2 x^2-x+1}{2 x}}-16 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^4\left (5^{\frac {1}{x}} e^{-\frac {1-x+2 x^2}{2 x}}-16 x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 28, normalized size = 0.97 \begin {gather*} \log ^4\left (e^{\frac {-1+x-2 x^2+\log (25)}{2 x}}-16 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 29, normalized size = 1.00 \begin {gather*} \log \left (-16 \, x^{4} + e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )^{4} \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 {2 \, {\left (128 \, x^{5} + {\left (2 \, x^{2} + 2 \, \log \relax (5) - 1\right )} e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )} \log \left (-16 \, x^{4} + e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )^{3}}{16 \, x^{6} - x^{2} e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 30, normalized size = 1.03
method | result | size |
risch | \(\ln \left ({\mathrm e}^{\frac {2 \ln \relax (5)-2 x^{2}+x -1}{2 x}}-16 x^{4}\right )^{4}-\frac {3}{2}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.77, size = 574, normalized size = 19.79 \begin {gather*} -2 \, {\left (\frac {2 \, x^{2} + 1}{x} - 2 \, \log \left (-{\left (16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} - e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )} e^{\left (-\frac {1}{2}\right )}\right )\right )} \log \left (-16 \, x^{4} + e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )^{3} - \frac {3 \, {\left (4 \, x^{4} + 4 \, x^{2} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{2} + 4 \, x^{3} - 4 \, {\left (2 \, x^{3} + x^{2} + x\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right ) + 2 \, x + 1\right )} \log \left (-16 \, x^{4} + e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )^{2}}{2 \, x^{2}} - \frac {{\left (8 \, x^{6} - 8 \, x^{3} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{3} + 12 \, x^{5} - 12 \, x^{4} + 12 \, {\left (2 \, x^{4} + x^{3} + x^{2}\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{2} - 6 \, x^{2} - 6 \, {\left (4 \, x^{5} + 4 \, x^{4} + 2 \, x^{2} + x\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right ) + 3 \, x + 1\right )} \log \left (-16 \, x^{4} + e^{\left (-\frac {2 \, x^{2} - x - 2 \, \log \relax (5) + 1}{2 \, x}\right )}\right )}{2 \, x^{3}} - \frac {16 \, x^{8} + 16 \, x^{4} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{4} + 32 \, x^{7} - 64 \, x^{6} - 48 \, x^{5} - 32 \, {\left (2 \, x^{5} + x^{4} + x^{3}\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{3} - 24 \, x^{3} + 24 \, {\left (4 \, x^{6} + 4 \, x^{5} + 2 \, x^{3} + x^{2}\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right )^{2} - 16 \, x^{2} - 8 \, {\left (8 \, x^{7} + 12 \, x^{6} - 12 \, x^{5} - 6 \, x^{3} + 3 \, x^{2} + x\right )} \log \left (-16 \, x^{4} e^{\left (x + \frac {1}{2 \, x}\right )} + e^{\left (\frac {\log \relax (5)}{x} + \frac {1}{2}\right )}\right ) + 4 \, x + 1}{16 \, x^{4}} \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 = -0.03 \begin {gather*} \int -\frac {{\ln \left ({\mathrm {e}}^{\frac {-x^2+\frac {x}{2}+\ln \relax (5)-\frac {1}{2}}{x}}-16\,x^4\right )}^3\,\left ({\mathrm {e}}^{\frac {-x^2+\frac {x}{2}+\ln \relax (5)-\frac {1}{2}}{x}}\,\left (4\,x^2+4\,\ln \relax (5)-2\right )+256\,x^5\right )}{x^2\,{\mathrm {e}}^{\frac {-x^2+\frac {x}{2}+\ln \relax (5)-\frac {1}{2}}{x}}-16\,x^6} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.63, size = 24, normalized size = 0.83 \begin {gather*} \log {\left (- 16 x^{4} + e^{\frac {- x^{2} + \frac {x}{2} - \frac {1}{2} + \log {\relax (5 )}}{x}} \right )}^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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