Optimal. Leaf size=24 \[ \log (4+x)+\log \left (\log \left (\log \left (25-2 \left (-5+\frac {2 e^3 x}{\log (3)}\right )\right )\right )\right ) \]
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Rubi [A]
time = 0.26, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 2, integrand size = 121, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6820, 6816}
\begin {gather*} \log (x+4)+\log \left (\log \left (\log \left (35-\frac {4 e^3 x}{\log (3)}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{4+x}+\frac {4 e^3}{\left (4 e^3 x-35 \log (3)\right ) \log \left (35-\frac {4 e^3 x}{\log (3)}\right ) \log \left (\log \left (35-\frac {4 e^3 x}{\log (3)}\right )\right )}\right ) \, dx\\ &=\log (4+x)+\left (4 e^3\right ) \int \frac {1}{\left (4 e^3 x-35 \log (3)\right ) \log \left (35-\frac {4 e^3 x}{\log (3)}\right ) \log \left (\log \left (35-\frac {4 e^3 x}{\log (3)}\right )\right )} \, dx\\ &=\log (4+x)+\log \left (\log \left (\log \left (35-\frac {4 e^3 x}{\log (3)}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 20, normalized size = 0.83 \begin {gather*} \log (4+x)+\log \left (\log \left (\log \left (35-\frac {4 e^3 x}{\log (3)}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 25, normalized size = 1.04
method | result | size |
norman | \(\ln \left (\ln \left (\ln \left (\frac {35 \ln \left (3\right )-4 x \,{\mathrm e}^{3}}{\ln \left (3\right )}\right )\right )\right )+\ln \left (4+x \right )\) | \(24\) |
risch | \(\ln \left (\ln \left (\ln \left (\frac {35 \ln \left (3\right )-4 x \,{\mathrm e}^{3}}{\ln \left (3\right )}\right )\right )\right )+\ln \left (4+x \right )\) | \(24\) |
default | \(\ln \left (4+x \right )+\ln \left (\ln \left (-\ln \left (\ln \left (3\right )\right )+\ln \left (35 \ln \left (3\right )-4 x \,{\mathrm e}^{3}\right )\right )\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 24, normalized size = 1.00 \begin {gather*} \log \left (x + 4\right ) + \log \left (\log \left (\log \left (-4 \, x e^{3} + 35 \, \log \left (3\right )\right ) - \log \left (\log \left (3\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 24, normalized size = 1.00 \begin {gather*} \log \left (x + 4\right ) + \log \left (\log \left (\log \left (-\frac {4 \, x e^{3} - 35 \, \log \left (3\right )}{\log \left (3\right )}\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 24, normalized size = 1.00 \begin {gather*} \log {\left (x + 4 \right )} + \log {\left (\log {\left (\log {\left (\frac {- 4 x e^{3} + 35 \log {\left (3 \right )}}{\log {\left (3 \right )}} \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 105 vs.
\(2 (19) = 38\).
time = 0.47, size = 105, normalized size = 4.38 \begin {gather*} \frac {35 \, \log \left (3\right ) \log \left (4 \, x e^{3} - 35 \, \log \left (3\right )\right ) - 35 \, \log \left (3\right ) \log \left (-4 \, x e^{3} + 35 \, \log \left (3\right )\right ) + 16 \, e^{3} \log \left (x + 4\right ) + 35 \, \log \left (3\right ) \log \left (x + 4\right ) + 16 \, e^{3} \log \left (\log \left (\log \left (-4 \, x e^{3} + 35 \, \log \left (3\right )\right ) - \log \left (\log \left (3\right )\right )\right )\right ) + 35 \, \log \left (3\right ) \log \left (\log \left (\log \left (-4 \, x e^{3} + 35 \, \log \left (3\right )\right ) - \log \left (\log \left (3\right )\right )\right )\right )}{16 \, e^{3} + 35 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.03, size = 24, normalized size = 1.00 \begin {gather*} \ln \left (x+4\right )+\ln \left (\ln \left (\ln \left (35\,\ln \left (3\right )-4\,x\,{\mathrm {e}}^3\right )-\ln \left (\ln \left (3\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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