Optimal. Leaf size=25 \[ \frac {1}{24} \log \left (9-x^3\right )-\frac {1}{24} \log \left (1-x^3\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {1352, 616, 31} \[ \frac {1}{24} \log \left (9-x^3\right )-\frac {1}{24} \log \left (1-x^3\right ) \]
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rule 1352
Rubi steps
\begin {align*} \int \frac {x^2}{9-10 x^3+x^6} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{9-10 x+x^2} \, dx,x,x^3\right )\\ &=\frac {1}{24} \operatorname {Subst}\left (\int \frac {1}{-9+x} \, dx,x,x^3\right )-\frac {1}{24} \operatorname {Subst}\left (\int \frac {1}{-1+x} \, dx,x,x^3\right )\\ &=-\frac {1}{24} \log \left (1-x^3\right )+\frac {1}{24} \log \left (9-x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \[ \frac {1}{24} \log \left (9-x^3\right )-\frac {1}{24} \log \left (1-x^3\right ) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 16, normalized size = 0.64 \[ \frac {1}{12} \tanh ^{-1}\left (\frac {5}{4}-\frac {x^3}{4}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.40, size = 17, normalized size = 0.68 \[ -\frac {1}{24} \, \log \left (x^{3} - 1\right ) + \frac {1}{24} \, \log \left (x^{3} - 9\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 19, normalized size = 0.76 \[ -\frac {1}{24} \, \log \left ({\left | x^{3} - 1 \right |}\right ) + \frac {1}{24} \, \log \left ({\left | x^{3} - 9 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 18, normalized size = 0.72
method | result | size |
default | \(\frac {\ln \left (x^{3}-9\right )}{24}-\frac {\ln \left (x^{3}-1\right )}{24}\) | \(18\) |
risch | \(\frac {\ln \left (x^{3}-9\right )}{24}-\frac {\ln \left (x^{3}-1\right )}{24}\) | \(18\) |
norman | \(-\frac {\ln \left (-1+x \right )}{24}+\frac {\ln \left (x^{3}-9\right )}{24}-\frac {\ln \left (x^{2}+x +1\right )}{24}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 17, normalized size = 0.68 \[ -\frac {1}{24} \, \log \left (x^{3} - 1\right ) + \frac {1}{24} \, \log \left (x^{3} - 9\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.58, size = 16, normalized size = 0.64 \[ \frac {\mathrm {atanh}\left (\frac {81}{320\,\left (\frac {5\,x^3}{4}-\frac {9}{8}\right )}-\frac {41}{40}\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.60 \[ \frac {\log {\left (x^{3} - 9 \right )}}{24} - \frac {\log {\left (x^{3} - 1 \right )}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
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