Optimal. Leaf size=15 \[ \frac {1}{2} \log \left (x^4-x^2+1\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1587} \[ \frac {1}{2} \log \left (x^4-x^2+1\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {align*} \int \frac {-x+2 x^3}{1-x^2+x^4} \, dx &=\frac {1}{2} \log \left (1-x^2+x^4\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {1}{2} \log \left (x^4-x^2+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 13, normalized size = 0.87 \[ \frac {1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 13, normalized size = 0.87 \[ \frac {1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \[ \frac {\ln \left (x^{4}-x^{2}+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 13, normalized size = 0.87 \[ \frac {1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 0.87 \[ \frac {\ln \left (x^4-x^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.67 \[ \frac {\log {\left (x^{4} - x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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