Optimal. Leaf size=12 \[ \frac {1}{18} \tanh ^{-1}\left (\frac {x^6}{3}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {275, 206} \[ \frac {1}{18} \tanh ^{-1}\left (\frac {x^6}{3}\right ) \]
Antiderivative was successfully verified.
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Rule 206
Rule 275
Rubi steps
\begin {align*} \int \frac {x^5}{9-x^{12}} \, dx &=\frac {1}{6} \operatorname {Subst}\left (\int \frac {1}{9-x^2} \, dx,x,x^6\right )\\ &=\frac {1}{18} \tanh ^{-1}\left (\frac {x^6}{3}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 1.92 \[ \frac {1}{36} \log \left (x^6+3\right )-\frac {1}{36} \log \left (3-x^6\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.89, size = 17, normalized size = 1.42 \[ \frac {1}{36} \, \log \left (x^{6} + 3\right ) - \frac {1}{36} \, \log \left (x^{6} - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 18, normalized size = 1.50 \[ \frac {1}{36} \, \log \left (x^{6} + 3\right ) - \frac {1}{36} \, \log \left ({\left | x^{6} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 18, normalized size = 1.50 \[ -\frac {\ln \left (x^{6}-3\right )}{36}+\frac {\ln \left (x^{6}+3\right )}{36} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.01, size = 17, normalized size = 1.42 \[ \frac {1}{36} \, \log \left (x^{6} + 3\right ) - \frac {1}{36} \, \log \left (x^{6} - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 8, normalized size = 0.67 \[ \frac {\mathrm {atanh}\left (\frac {x^6}{3}\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 15, normalized size = 1.25 \[ - \frac {\log {\left (x^{6} - 3 \right )}}{36} + \frac {\log {\left (x^{6} + 3 \right )}}{36} \]
Verification of antiderivative is not currently implemented for this CAS.
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