Optimal. Leaf size=29 \[ \log \left (3 e^2 \left (\frac {1+\frac {5+\frac {-3+x}{x}}{x}}{x}+x^2\right )\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 21, normalized size of antiderivative = 0.72, number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {2074, 1587} \begin {gather*} \log \left (-x^5-x^2-6 x+3\right )-3 \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 {3}{x}+\frac {6+2 x+5 x^4}{-3+6 x+x^2+x^5}\right ) \, dx\\ &=-3 \log (x)+\int \frac {6+2 x+5 x^4}{-3+6 x+x^2+x^5} \, dx\\ &=-3 \log (x)+\log \left (3-6 x-x^2-x^5\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.72 \begin {gather*} -3 \log (x)+\log \left (3-6 x-x^2-x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 17, normalized size = 0.59 \begin {gather*} \log \left (x^{5} + x^{2} + 6 \, x - 3\right ) - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 19, normalized size = 0.66 \begin {gather*} \log \left ({\left | x^{5} + x^{2} + 6 \, x - 3 \right |}\right ) - 3 \, \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 = 0.02, size = 18, normalized size = 0.62
method | result | size |
default | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \relax (x )\) | \(18\) |
norman | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \relax (x )\) | \(18\) |
risch | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \relax (x )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 17, normalized size = 0.59 \begin {gather*} \log \left (x^{5} + x^{2} + 6 \, x - 3\right ) - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 17, normalized size = 0.59 \begin {gather*} \ln \left (x^5+x^2+6\,x-3\right )-3\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.59 \begin {gather*} - 3 \log {\relax (x )} + \log {\left (x^{5} + x^{2} + 6 x - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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