Optimal. Leaf size=11 \[ -4+e^2+\log (-4+x+\log (x)) \]
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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+x}{-4 x+x^2+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}{-4+x+\log (x)}+\frac {1}{x (-4+x+\log (x))}\right ) \, dx\\ &=\int \frac {1}{-4+x+\log (x)} \, dx+\int \frac {1}{x (-4+x+\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 10, normalized size = 0.91 \begin {gather*} \log (4-x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 6, normalized size = 0.55 \begin {gather*} \log \left (x + \log \relax (x) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 6, normalized size = 0.55 \begin {gather*} \log \left (x + \log \relax (x) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.64
method | result | size |
norman | \(\ln \left (x +\ln \relax (x )-4\right )\) | \(7\) |
risch | \(\ln \left (x +\ln \relax (x )-4\right )\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 6, normalized size = 0.55 \begin {gather*} \log \left (x + \log \relax (x) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.06, size = 6, normalized size = 0.55 \begin {gather*} \ln \left (x+\ln \relax (x)-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 7, normalized size = 0.64 \begin {gather*} \log {\left (x + \log {\relax (x )} - 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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