Optimal. Leaf size=12 \[ \log \left ((-3+x)^2-\frac {5}{x}\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.75, number of steps
used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2099, 1601}
\begin {gather*} \log \left (-x^3+6 x^2-9 x+5\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x}+\frac {3 \left (3-4 x+x^2\right )}{-5+9 x-6 x^2+x^3}\right ) \, dx\\ &=-\log (x)+3 \int \frac {3-4 x+x^2}{-5+9 x-6 x^2+x^3} \, dx\\ &=-\log (x)+\log \left (5-9 x+6 x^2-x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.75 \begin {gather*} -\log (x)+\log \left (5-9 x+6 x^2-x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 20, normalized size = 1.67
method | result | size |
default | \(-\ln \left (x \right )+\ln \left (x^{3}-6 x^{2}+9 x -5\right )\) | \(20\) |
norman | \(-\ln \left (x \right )+\ln \left (x^{3}-6 x^{2}+9 x -5\right )\) | \(20\) |
risch | \(-\ln \left (x \right )+\ln \left (x^{3}-6 x^{2}+9 x -5\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 1.58 \begin {gather*} \log \left (x^{3} - 6 \, x^{2} + 9 \, x - 5\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 19, normalized size = 1.58 \begin {gather*} \log \left (x^{3} - 6 \, x^{2} + 9 \, x - 5\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 17 vs.
\(2 (8) = 16\).
time = 0.04, size = 17, normalized size = 1.42 \begin {gather*} - \log {\left (x \right )} + \log {\left (x^{3} - 6 x^{2} + 9 x - 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 21, normalized size = 1.75 \begin {gather*} \log \left ({\left | x^{3} - 6 \, x^{2} + 9 \, x - 5 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 19, normalized size = 1.58 \begin {gather*} \ln \left (x^3-6\,x^2+9\,x-5\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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