Optimal. Leaf size=22 \[ \frac {-2 x+\frac {e^{-4 e^5} \log (3)}{x}}{\log (5)} \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 14} \begin {gather*} \frac {e^{-4 e^5} \log (3)}{x \log (5)}-\frac {2 x}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-4 e^5} \int \frac {-2 e^{4 e^5} x^2-\log (3)}{x^2} \, dx}{\log (5)}\\ &=\frac {e^{-4 e^5} \int \left (-2 e^{4 e^5}-\frac {\log (3)}{x^2}\right ) \, dx}{\log (5)}\\ &=-\frac {2 x}{\log (5)}+\frac {e^{-4 e^5} \log (3)}{x \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.09 \begin {gather*} -\frac {2 x-\frac {e^{-4 e^5} \log (3)}{x}}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 29, normalized size = 1.32 \begin {gather*} -\frac {{\left (2 \, x^{2} e^{\left (4 \, e^{5}\right )} - \log \relax (3)\right )} e^{\left (-4 \, e^{5}\right )}}{x \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 27, normalized size = 1.23 \begin {gather*} -\frac {{\left (2 \, x e^{\left (4 \, e^{5}\right )} - \frac {\log \relax (3)}{x}\right )} e^{\left (-4 \, e^{5}\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 24, normalized size = 1.09
method | result | size |
risch | \(-\frac {2 x}{\ln \relax (5)}+\frac {{\mathrm e}^{-4 \,{\mathrm e}^{5}} \ln \relax (3)}{\ln \relax (5) x}\) | \(24\) |
norman | \(\frac {\frac {{\mathrm e}^{-4 \,{\mathrm e}^{5}} \ln \relax (3)}{\ln \relax (5)}-\frac {2 x^{2}}{\ln \relax (5)}}{x}\) | \(27\) |
default | \(\frac {{\mathrm e}^{-4 \,{\mathrm e}^{5}} \left (-2 x \,{\mathrm e}^{4 \,{\mathrm e}^{5}}+\frac {\ln \relax (3)}{x}\right )}{\ln \relax (5)}\) | \(28\) |
gosper | \(\frac {\left (-2 x^{2} {\mathrm e}^{4 \,{\mathrm e}^{5}}+\ln \relax (3)\right ) {\mathrm e}^{-4 \,{\mathrm e}^{5}}}{x \ln \relax (5)}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 27, normalized size = 1.23 \begin {gather*} -\frac {{\left (2 \, x e^{\left (4 \, e^{5}\right )} - \frac {\log \relax (3)}{x}\right )} e^{\left (-4 \, e^{5}\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 26, normalized size = 1.18 \begin {gather*} \frac {{\mathrm {e}}^{-4\,{\mathrm {e}}^5}\,\left (\ln \relax (3)-2\,x^2\,{\mathrm {e}}^{4\,{\mathrm {e}}^5}\right )}{x\,\ln \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 24, normalized size = 1.09 \begin {gather*} \frac {- 2 x e^{4 e^{5}} + \frac {\log {\relax (3 )}}{x}}{e^{4 e^{5}} \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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