Optimal. Leaf size=17 \[ -\log (3 (1+\log (x)))+\log \left (x^3+\log (x)\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps
used = 5, number of rules used = 4, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.114, Rules used = {6874, 2339, 29,
6816} \begin {gather*} \log \left (x^3+\log (x)\right )-\log (\log (x)+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 6816
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x (1+\log (x))}+\frac {1+3 x^3}{x \left (x^3+\log (x)\right )}\right ) \, dx\\ &=-\int \frac {1}{x (1+\log (x))} \, dx+\int \frac {1+3 x^3}{x \left (x^3+\log (x)\right )} \, dx\\ &=\log \left (x^3+\log (x)\right )-\text {Subst}\left (\int \frac {1}{x} \, dx,x,1+\log (x)\right )\\ &=-\log (1+\log (x))+\log \left (x^3+\log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} -\log (1+\log (x))+\log \left (x^3+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 4.08, size = 16, normalized size = 0.94
method | result | size |
default | \(-\ln \left (\ln \left (x \right )+1\right )+\ln \left (\ln \left (x \right )+x^{3}\right )\) | \(16\) |
norman | \(-\ln \left (\ln \left (x \right )+1\right )+\ln \left (\ln \left (x \right )+x^{3}\right )\) | \(16\) |
risch | \(-\ln \left (\ln \left (x \right )+1\right )+\ln \left (\ln \left (x \right )+x^{3}\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 15, normalized size = 0.88 \begin {gather*} \log \left (x^{3} + \log \left (x\right )\right ) - \log \left (\log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 15, normalized size = 0.88 \begin {gather*} \log \left (x^{3} + \log \left (x\right )\right ) - \log \left (\log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 14, normalized size = 0.82 \begin {gather*} \log {\left (x^{3} + \log {\left (x \right )} \right )} - \log {\left (\log {\left (x \right )} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 15, normalized size = 0.88 \begin {gather*} \log \left (x^{3} + \log \left (x\right )\right ) - \log \left (\log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.18, size = 15, normalized size = 0.88 \begin {gather*} \ln \left (\ln \left (x\right )+x^3\right )-\ln \left (\ln \left (x\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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