Optimal. Leaf size=25 \[ 3+e^5+x+6 \left (4+e^5+\log \left (\left (5-x^2+\log (x)\right )^2\right )\right ) \]
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Rubi [A] time = 0.24, antiderivative size = 14, normalized size of antiderivative = 0.56, number of steps used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6742, 6684} \begin {gather*} 12 \log \left (-x^2+\log (x)+5\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {12 \left (-1+2 x^2\right )}{x \left (-5+x^2-\log (x)\right )}\right ) \, dx\\ &=x+12 \int \frac {-1+2 x^2}{x \left (-5+x^2-\log (x)\right )} \, dx\\ &=x+12 \log \left (5-x^2+\log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 14, normalized size = 0.56 \begin {gather*} x+12 \log \left (5-x^2+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 14, normalized size = 0.56 \begin {gather*} x + 12 \, \log \left (-x^{2} + \log \relax (x) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 14, normalized size = 0.56 \begin {gather*} x + 12 \, \log \left (-x^{2} + \log \relax (x) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 0.60
method | result | size |
norman | \(x +12 \ln \left (-\ln \relax (x )+x^{2}-5\right )\) | \(15\) |
risch | \(x +12 \ln \left (\ln \relax (x )-x^{2}+5\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 14, normalized size = 0.56 \begin {gather*} x + 12 \, \log \left (-x^{2} + \log \relax (x) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.25, size = 14, normalized size = 0.56 \begin {gather*} x+12\,\ln \left (x^2-\ln \relax (x)-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.48 \begin {gather*} x + 12 \log {\left (- x^{2} + \log {\relax (x )} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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