Optimal. Leaf size=15 \[ \frac{1}{2} \log \left (x^4-x^2+1\right ) \]
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Rubi [A] time = 0.0092598, antiderivative size = 15, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0061354, size = 15, normalized size = 1. \[ \frac{1}{2} \log \left (x^4-x^2+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \begin{align*}{\frac{\ln \left ({x}^{4}-{x}^{2}+1 \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924786, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81189, size = 32, normalized size = 2.13 \begin{align*} \frac{1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.083604, size = 10, normalized size = 0.67 \begin{align*} \frac{\log{\left (x^{4} - x^{2} + 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06469, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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