Optimal. Leaf size=23 \[ \log \left (\frac {1-(6+x) \left (4+x-4 x^2\right )}{4 x}\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2074, 1587} \begin {gather*} \log \left (-4 x^3-23 x^2+10 x+23\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x}+\frac {2 \left (-5+23 x+6 x^2\right )}{-23-10 x+23 x^2+4 x^3}\right ) \, dx\\ &=-\log (x)+2 \int \frac {-5+23 x+6 x^2}{-23-10 x+23 x^2+4 x^3} \, dx\\ &=-\log (x)+\log \left (23+10 x-23 x^2-4 x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.91 \begin {gather*} -\log (x)+\log \left (23+10 x-23 x^2-4 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 21, normalized size = 0.91 \begin {gather*} \log \left (4 \, x^{3} + 23 \, x^{2} - 10 \, x - 23\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 23, normalized size = 1.00 \begin {gather*} \log \left ({\left | 4 \, x^{3} + 23 \, x^{2} - 10 \, x - 23 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 0.96
method | result | size |
default | \(-\ln \relax (x )+\ln \left (4 x^{3}+23 x^{2}-10 x -23\right )\) | \(22\) |
norman | \(-\ln \relax (x )+\ln \left (4 x^{3}+23 x^{2}-10 x -23\right )\) | \(22\) |
risch | \(-\ln \relax (x )+\ln \left (4 x^{3}+23 x^{2}-10 x -23\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 21, normalized size = 0.91 \begin {gather*} \log \left (4 \, x^{3} + 23 \, x^{2} - 10 \, x - 23\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 21, normalized size = 0.91 \begin {gather*} \ln \left (4\,x^3+23\,x^2-10\,x-23\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 0.83 \begin {gather*} - \log {\relax (x )} + \log {\left (4 x^{3} + 23 x^{2} - 10 x - 23 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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