Optimal. Leaf size=17 \[ 3 \log (x)-\log \left (x+2 x^3+\log (x)\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6874, 6816}
\begin {gather*} 3 \log (x)-\log \left (2 x^3+x+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (\frac {3}{x}+\frac {-1-x-6 x^3}{x \left (x+2 x^3+\log (x)\right )}\right ) \, dx\\ &=3 \log (x)+\int \frac {-1-x-6 x^3}{x \left (x+2 x^3+\log (x)\right )} \, dx\\ &=3 \log (x)-\log \left (x+2 x^3+\log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 17, normalized size = 1.00 \begin {gather*} 3 \log (x)-\log \left (x+2 x^3+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 18, normalized size = 1.06
method | result | size |
default | \(3 \ln \left (x \right )-\ln \left (x +2 x^{3}+\ln \left (x \right )\right )\) | \(18\) |
norman | \(3 \ln \left (x \right )-\ln \left (x +2 x^{3}+\ln \left (x \right )\right )\) | \(18\) |
risch | \(3 \ln \left (x \right )-\ln \left (x +2 x^{3}+\ln \left (x \right )\right )\) | \(18\) |
parallelrisch | \(-\ln \left (x^{3}+\frac {x}{2}+\frac {\ln \left (x \right )}{2}\right )+3 \ln \left (x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 17, normalized size = 1.00 \begin {gather*} -\log \left (2 \, x^{3} + x + \log \left (x\right )\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.59, size = 17, normalized size = 1.00 \begin {gather*} -\log \left (2 \, x^{3} + x + \log \left (x\right )\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 15, normalized size = 0.88 \begin {gather*} 3 \log {\left (x \right )} - \log {\left (2 x^{3} + x + \log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 21, normalized size = 1.24 \begin {gather*} -\log \left (-2 \, x^{3} - x - \log \left (x\right )\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.21, size = 17, normalized size = 1.00 \begin {gather*} 3\,\ln \left (x\right )-\ln \left (x+\ln \left (x\right )+2\,x^3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 17, normalized size = 1.00 \begin {gather*} 3 \ln \left (x \right )+\arctan \left (x^{2}\right )-\ln \left (x^{2}+1\right ) \end {gather*}
Warning: Unable to verify antiderivative.
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