Optimal. Leaf size=20 \[ 4 \log \left (e^{12+2 x}-\log (\log (2+10 x))\right ) \]
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Rubi [A]
time = 0.33, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6873, 6816}
\begin {gather*} 4 \log \left (e^{2 x+12}-\log (\log (10 x+2))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20-e^{12+2 x} (-8-40 x) \log (2+10 x)}{(1+5 x) \log (2+10 x) \left (e^{12+2 x}-\log (\log (2+10 x))\right )} \, dx\\ &=4 \log \left (e^{12+2 x}-\log (\log (2+10 x))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 20, normalized size = 1.00 \begin {gather*} 4 \log \left (e^{2 (6+x)}-\log (\log (2+10 x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 20, normalized size = 1.00
method | result | size |
risch | \(4 \ln \left (-{\mathrm e}^{2 x +12}+\ln \left (\ln \left (10 x +2\right )\right )\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 22, normalized size = 1.10 \begin {gather*} 4 \, \log \left (-e^{\left (2 \, x + 12\right )} + \log \left (\log \left (2\right ) + \log \left (5 \, x + 1\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 19, normalized size = 0.95 \begin {gather*} 4 \, \log \left (-e^{\left (2 \, x + 12\right )} + \log \left (\log \left (10 \, x + 2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 17, normalized size = 0.85 \begin {gather*} 4 \log {\left (e^{2 x + 12} - \log {\left (\log {\left (10 x + 2 \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 19, normalized size = 0.95 \begin {gather*} 4 \, \log \left (-e^{\left (2 \, x + 12\right )} + \log \left (\log \left (10 \, x + 2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.22, size = 19, normalized size = 0.95 \begin {gather*} 4\,\ln \left (\ln \left (\ln \left (10\,x+2\right )\right )-{\mathrm {e}}^{2\,x+12}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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