Optimal. Leaf size=16 \[ \log \left (-3 x-15 x^2 \log (2 (3+x))\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps
used = 2, number of rules used = 2, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6873, 6817}
\begin {gather*} \log (x (5 x \log (2 (x+3))+1)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6817
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+x+5 x^2+\left (30 x+10 x^2\right ) \log (6+2 x)}{x (3+x) (1+5 x \log (2 (3+x)))} \, dx\\ &=\log (x (1+5 x \log (2 (3+x))))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 15, normalized size = 0.94 \begin {gather*} \log (x)+\log (1+5 x \log (2 (3+x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(41\) vs.
\(2(16)=32\).
time = 0.07, size = 42, normalized size = 2.62
method | result | size |
norman | \(\ln \left (x \right )+\ln \left (5 x \ln \left (2 x +6\right )+1\right )\) | \(16\) |
risch | \(2 \ln \left (x \right )+\ln \left (\ln \left (2 x +6\right )+\frac {1}{5 x}\right )\) | \(19\) |
derivativedivides | \(\ln \left (5 \ln \left (2 x +6\right ) \left (2 x +6\right )^{2}-60 \ln \left (2 x +6\right ) \left (2 x +6\right )+180 \ln \left (2 x +6\right )+4 x \right )\) | \(42\) |
default | \(\ln \left (5 \ln \left (2 x +6\right ) \left (2 x +6\right )^{2}-60 \ln \left (2 x +6\right ) \left (2 x +6\right )+180 \ln \left (2 x +6\right )+4 x \right )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 25, normalized size = 1.56 \begin {gather*} 2 \, \log \left (x\right ) + \log \left (\frac {5 \, x \log \left (2\right ) + 5 \, x \log \left (x + 3\right ) + 1}{5 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 21, normalized size = 1.31 \begin {gather*} 2 \, \log \left (x\right ) + \log \left (\frac {5 \, x \log \left (2 \, x + 6\right ) + 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 17, normalized size = 1.06 \begin {gather*} 2 \log {\left (x \right )} + \log {\left (\log {\left (2 x + 6 \right )} + \frac {1}{5 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.94 \begin {gather*} \log \left (5 \, x \log \left (2 \, x + 6\right ) + 1\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.40, size = 15, normalized size = 0.94 \begin {gather*} \ln \left (5\,x\,\ln \left (2\,x+6\right )+1\right )+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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