Optimal. Leaf size=25 \[ \log \left (-x+\frac {1+e^{\frac {6}{e^{20}}}-\frac {x^2}{25}}{x}\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 5, number of rules used = 4, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6, 1593, 446, 72} \begin {gather*} \log \left (25 \left (1+e^{\frac {6}{e^{20}}}\right )-26 x^2\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 72
Rule 446
Rule 1593
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-25-25 e^{\frac {6}{e^{20}}}-26 x^2}{\left (25+25 e^{\frac {6}{e^{20}}}\right ) x-26 x^3} \, dx\\ &=\int \frac {-25-25 e^{\frac {6}{e^{20}}}-26 x^2}{x \left (25+25 e^{\frac {6}{e^{20}}}-26 x^2\right )} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {-25-25 e^{\frac {6}{e^{20}}}-26 x}{\left (25+25 e^{\frac {6}{e^{20}}}-26 x\right ) x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (-\frac {52}{25+25 e^{\frac {6}{e^{20}}}-26 x}-\frac {1}{x}\right ) \, dx,x,x^2\right )\\ &=-\log (x)+\log \left (25 \left (1+e^{\frac {6}{e^{20}}}\right )-26 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 22, normalized size = 0.88 \begin {gather*} -\log (x)+\log \left (25+25 e^{\frac {6}{e^{20}}}-26 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 20, normalized size = 0.80 \begin {gather*} \log \left (26 \, x^{2} - 25 \, e^{\left (6 \, e^{\left (-20\right )}\right )} - 25\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 23, normalized size = 0.92 \begin {gather*} -\frac {1}{2} \, \log \left (x^{2}\right ) + \log \left ({\left | 26 \, x^{2} - 25 \, e^{\left (6 \, e^{\left (-20\right )}\right )} - 25 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.47, size = 21, normalized size = 0.84
method | result | size |
default | \(-\ln \relax (x )+\ln \left (26 x^{2}-25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}-25\right )\) | \(21\) |
risch | \(-\ln \relax (x )+\ln \left (26 x^{2}-25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}-25\right )\) | \(21\) |
norman | \(-\ln \relax (x )+\ln \left (-26 x^{2}+25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}+25\right )\) | \(23\) |
meijerg | \(-\frac {25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}} \left (-\ln \left (1-\frac {26 x^{2}}{25 \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}\right )+2 \ln \relax (x )+\ln \relax (2)+\ln \left (13\right )-2 \ln \relax (5)-\ln \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )+i \pi \right )}{2 \left (25+25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}+\frac {25 \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right ) \ln \left (1-\frac {26 x^{2}}{25 \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}\right )}{2 \left (25+25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}-\frac {25 \left (-\ln \left (1-\frac {26 x^{2}}{25 \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}\right )+2 \ln \relax (x )+\ln \relax (2)+\ln \left (13\right )-2 \ln \relax (5)-\ln \left (1+{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )+i \pi \right )}{2 \left (25+25 \,{\mathrm e}^{6 \,{\mathrm e}^{-20}}\right )}\) | \(162\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 20, normalized size = 0.80 \begin {gather*} \log \left (26 \, x^{2} - 25 \, e^{\left (6 \, e^{\left (-20\right )}\right )} - 25\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 20, normalized size = 0.80 \begin {gather*} \ln \left (-52\,x^2+50\,{\mathrm {e}}^{6\,{\mathrm {e}}^{-20}}+50\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 20, normalized size = 0.80 \begin {gather*} - \log {\relax (x )} + \log {\left (x^{2} - \frac {25 e^{\frac {6}{e^{20}}}}{26} - \frac {25}{26} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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