Optimal. Leaf size=17 \[ 5+\log \left (\log \left (2+\frac {1}{5} x^2 \log (3+x)\right )\right ) \]
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Rubi [A]
time = 0.05, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 1, number of rules used = 1, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6816}
\begin {gather*} \log \left (\log \left (\frac {1}{5} \left (x^2 \log (x+3)+10\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (\frac {1}{5} \left (10+x^2 \log (3+x)\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} \log \left (\log \left (2+\frac {1}{5} x^2 \log (3+x)\right )\right ) \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. \(34\) vs.
\(2(15)=30\).
time = 0.85, size = 35, normalized size = 2.06
method | result | size |
risch | \(\ln \left (\ln \left (\frac {\ln \left (3+x \right ) x^{2}}{5}+2\right )\right )\) | \(14\) |
default | \(\ln \left (\ln \left (5\right )-\ln \left (\left (3+x \right )^{2} \ln \left (3+x \right )-6 \left (3+x \right ) \ln \left (3+x \right )+9 \ln \left (3+x \right )+10\right )\right )\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 17, normalized size = 1.00 \begin {gather*} \log \left (-\log \left (5\right ) + \log \left (x^{2} \log \left (x + 3\right ) + 10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 13, normalized size = 0.76 \begin {gather*} \log \left (\log \left (\frac {1}{5} \, x^{2} \log \left (x + 3\right ) + 2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 14, normalized size = 0.82 \begin {gather*} \log {\left (\log {\left (\frac {x^{2} \log {\left (x + 3 \right )}}{5} + 2 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 1.00 \begin {gather*} \log \left (\log \left (5\right ) - \log \left (x^{2} \log \left (x + 3\right ) + 10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.08, size = 13, normalized size = 0.76 \begin {gather*} \ln \left (\ln \left (\frac {x^2\,\ln \left (x+3\right )}{5}+2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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