Optimal. Leaf size=33 \[ e^{\frac {8}{i \pi +\log (-\log (\log (2)))}}+\log \left (\frac {e^{e^5}}{x}-x\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 17, normalized size of antiderivative = 0.52, number of steps
used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {1607, 457, 78}
\begin {gather*} \log \left (e^{e^5}-x^2\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rule 457
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{e^5}-x^2}{x \left (e^{e^5}-x^2\right )} \, dx\\ &=\frac {1}{2} \text {Subst}\left (\int \frac {-e^{e^5}-x}{\left (e^{e^5}-x\right ) x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \text {Subst}\left (\int \left (-\frac {2}{e^{e^5}-x}-\frac {1}{x}\right ) \, dx,x,x^2\right )\\ &=-\log (x)+\log \left (e^{e^5}-x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 0.52 \begin {gather*} -\log (x)+\log \left (e^{e^5}-x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 16, normalized size = 0.48
method | result | size |
default | \(\ln \left (x^{2}-{\mathrm e}^{{\mathrm e}^{5}}\right )-\ln \left (x \right )\) | \(16\) |
norman | \(-\ln \left (x \right )+\ln \left (-x^{2}+{\mathrm e}^{{\mathrm e}^{5}}\right )\) | \(16\) |
risch | \(\ln \left (x^{2}-{\mathrm e}^{{\mathrm e}^{5}}\right )-\ln \left (x \right )\) | \(16\) |
meijerg | \(\ln \left (1-x^{2} {\mathrm e}^{-{\mathrm e}^{5}}\right )-\ln \left (x \right )+\frac {{\mathrm e}^{5}}{2}-\frac {i \pi }{2}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 15, normalized size = 0.45 \begin {gather*} \log \left (x^{2} - e^{\left (e^{5}\right )}\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.45 \begin {gather*} \log \left (x^{2} - e^{\left (e^{5}\right )}\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 12, normalized size = 0.36 \begin {gather*} - \log {\left (x \right )} + \log {\left (x^{2} - e^{e^{5}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 18, normalized size = 0.55 \begin {gather*} -\frac {1}{2} \, \log \left (x^{2}\right ) + \log \left ({\left | x^{2} - e^{\left (e^{5}\right )} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.03, size = 15, normalized size = 0.45 \begin {gather*} \ln \left (x^2-{\mathrm {e}}^{{\mathrm {e}}^5}\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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