Optimal. Leaf size=12 \[ \log \left (3-x^2-\log (x)\right ) \]
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Rubi [F]
time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {1+2 x^2}{-3 x+x^3+x \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x \left (-3+x^2+\log (x)\right )}+\frac {2 x}{-3+x^2+\log (x)}\right ) \, dx\\ &=2 \int \frac {x}{-3+x^2+\log (x)} \, dx+\int \frac {1}{x \left (-3+x^2+\log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 8, normalized size = 0.67 \begin {gather*} \log \left (-3+x^2+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.09, size = 9, normalized size = 0.75
method | result | size |
default | \(\ln \left (x^{2}+\ln \left (x \right )-3\right )\) | \(9\) |
norman | \(\ln \left (x^{2}+\ln \left (x \right )-3\right )\) | \(9\) |
risch | \(\ln \left (x^{2}+\ln \left (x \right )-3\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 8, normalized size = 0.67 \begin {gather*} \log \left (x^{2} + \log \left (x\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 8, normalized size = 0.67 \begin {gather*} \log \left (x^{2} + \log \left (x\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} \log {\left (x^{2} + \log {\left (x \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 8, normalized size = 0.67 \begin {gather*} \log \left (x^{2} + \log \left (x\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.21, size = 8, normalized size = 0.67 \begin {gather*} \ln \left (\ln \left (x\right )+x^2-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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