Optimal. Leaf size=19 \[ 16+\log \left (\frac {1}{5 \left (e^3-x\right ) x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.74, number of steps
used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {642}
\begin {gather*} -\log \left (e^3 x-x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (e^3 x-x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} -\log \left (e^3-x\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.74, size = 12, normalized size = 0.63
method | result | size |
default | \(-\ln \left (x \left (-x +{\mathrm e}^{3}\right )\right )\) | \(12\) |
risch | \(-\ln \left (-x \,{\mathrm e}^{3}+x^{2}\right )\) | \(13\) |
norman | \(-\ln \left (x \right )-\ln \left (-x +{\mathrm e}^{3}\right )\) | \(15\) |
meijerg | \(-\ln \left (1-{\mathrm e}^{-3} x \right )-\ln \left (x \right )+3-i \pi \) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.63 \begin {gather*} -\log \left (x^{2} - x e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 12, normalized size = 0.63 \begin {gather*} -\log \left (x^{2} - x e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 10, normalized size = 0.53 \begin {gather*} - \log {\left (x^{2} - x e^{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.68 \begin {gather*} -\log \left ({\left | x^{2} - x e^{3} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 11, normalized size = 0.58 \begin {gather*} -\ln \left (x\,\left (x-{\mathrm {e}}^3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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