Optimal. Leaf size=19 \[ \log \left (6-\frac {x+\frac {1}{2} (5+x+\log (5))}{e^3}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps
used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 31}
\begin {gather*} \log \left (3 x-12 e^3+5+\log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 \int \frac {1}{5-12 e^3+3 x+\log (5)} \, dx\\ &=\log \left (5-12 e^3+3 x+\log (5)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} \log \left (5-12 e^3+3 x+\log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.69, size = 13, normalized size = 0.68
method | result | size |
default | \(\ln \left (\ln \left (5\right )-12 \,{\mathrm e}^{3}+3 x +5\right )\) | \(13\) |
risch | \(\ln \left (\ln \left (5\right )-12 \,{\mathrm e}^{3}+3 x +5\right )\) | \(13\) |
norman | \(\ln \left (-\ln \left (5\right )+12 \,{\mathrm e}^{3}-3 x -5\right )\) | \(15\) |
meijerg | \(\frac {3 \left (\frac {\ln \left (5\right )}{3}-4 \,{\mathrm e}^{3}+\frac {5}{3}\right ) \ln \left (1+\frac {3 x}{\ln \left (5\right )-12 \,{\mathrm e}^{3}+5}\right )}{\ln \left (5\right )-12 \,{\mathrm e}^{3}+5}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.63 \begin {gather*} \log \left (3 \, x - 12 \, e^{3} + \log \left (5\right ) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 12, normalized size = 0.63 \begin {gather*} \log \left (3 \, x - 12 \, e^{3} + \log \left (5\right ) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 0.74 \begin {gather*} \log {\left (3 x - 12 e^{3} + \log {\left (5 \right )} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 13, normalized size = 0.68 \begin {gather*} \log \left ({\left | 3 \, x - 12 \, e^{3} + \log \left (5\right ) + 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 12, normalized size = 0.63 \begin {gather*} \ln \left (3\,x-12\,{\mathrm {e}}^3+\ln \left (5\right )+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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