Optimal. Leaf size=18 \[ \frac {\log \left (e^{e^2}-x\right )}{-1+e^4} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {6, 31} \begin {gather*} -\frac {\log \left (e^{e^2}-x\right )}{1-e^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\int \frac {1}{e^{e^2} \left (-1+e^4\right )+\left (1-e^4\right ) x} \, dx\\ &=-\frac {\log \left (e^{e^2}-x\right )}{1-e^4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {\log \left (e^{e^2}-x\right )}{-1+e^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 15, normalized size = 0.83 \begin {gather*} \frac {\log \left (x - e^{\left (e^{2}\right )}\right )}{e^{4} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 26, normalized size = 1.44 \begin {gather*} \frac {\log \left ({\left | x e^{4} - {\left (e^{4} - 1\right )} e^{\left (e^{2}\right )} - x \right |}\right )}{e^{4} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 16, normalized size = 0.89
method | result | size |
norman | \(\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{2}}-x \right )}{{\mathrm e}^{4}-1}\) | \(16\) |
risch | \(\frac {\ln \left (-{\mathrm e}^{{\mathrm e}^{2}}+x \right )}{{\mathrm e}^{4}-1}\) | \(16\) |
meijerg | \(\frac {\ln \left (1-x \,{\mathrm e}^{-{\mathrm e}^{2}}\right )}{{\mathrm e}^{4}-1}\) | \(19\) |
default | \(-\frac {\ln \left (\left (1-{\mathrm e}^{4}\right ) x +\left ({\mathrm e}^{4}-1\right ) {\mathrm e}^{{\mathrm e}^{2}}\right )}{1-{\mathrm e}^{4}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 25, normalized size = 1.39 \begin {gather*} \frac {\log \left (x e^{4} - {\left (e^{4} - 1\right )} e^{\left (e^{2}\right )} - x\right )}{e^{4} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 15, normalized size = 0.83 \begin {gather*} \frac {\ln \left (x-{\mathrm {e}}^{{\mathrm {e}}^2}\right )}{{\mathrm {e}}^4-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 26, normalized size = 1.44 \begin {gather*} \frac {\log {\left (x \left (-1 + e^{4}\right ) - e^{4} e^{e^{2}} + e^{e^{2}} \right )}}{-1 + e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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