Optimal. Leaf size=8 \[ -\frac {1}{2} \tanh ^{-1}\left (x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {275, 207} \[ -\frac {1}{2} \tanh ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
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Rule 207
Rule 275
Rubi steps
\begin {align*} \int \frac {x}{-1+x^4} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{-1+x^2} \, dx,x,x^2\right )\\ &=-\frac {1}{2} \tanh ^{-1}\left (x^2\right )\\ \end {align*}
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Mathematica [B] time = 0.00, size = 23, normalized size = 2.88 \[ \frac {1}{4} \log \left (1-x^2\right )-\frac {1}{4} \log \left (x^2+1\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 17, normalized size = 2.12 \[ -\frac {1}{4} \, \log \left (x^{2} + 1\right ) + \frac {1}{4} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.01, size = 18, normalized size = 2.25 \[ -\frac {1}{4} \, \log \left (x^{2} + 1\right ) + \frac {1}{4} \, \log \left ({\left | x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 22, normalized size = 2.75 \[ \frac {\ln \left (x -1\right )}{4}+\frac {\ln \left (x +1\right )}{4}-\frac {\ln \left (x^{2}+1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 17, normalized size = 2.12 \[ -\frac {1}{4} \, \log \left (x^{2} + 1\right ) + \frac {1}{4} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 6, normalized size = 0.75 \[ -\frac {\mathrm {atanh}\left (x^2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.10, size = 15, normalized size = 1.88 \[ \frac {\log {\left (x^{2} - 1 \right )}}{4} - \frac {\log {\left (x^{2} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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