Optimal. Leaf size=17 \[ \frac{1}{4} \log \left (x^4+2 x^2+4 x\right ) \]
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Rubi [A] time = 0.0092228, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1587} \[ \frac{1}{4} \log \left (x^4+2 x^2+4 x\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin{align*} \int \frac{1+x+x^3}{4 x+2 x^2+x^4} \, dx &=\frac{1}{4} \log \left (4 x+2 x^2+x^4\right )\\ \end{align*}
Mathematica [A] time = 0.005459, size = 20, normalized size = 1.18 \[ \frac{1}{4} \log \left (x^3+2 x+4\right )+\frac{\log (x)}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( x \left ({x}^{3}+2\,x+4 \right ) \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937277, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.88942, size = 38, normalized size = 2.24 \begin{align*} \frac{1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091942, size = 14, normalized size = 0.82 \begin{align*} \frac{\log{\left (x^{4} + 2 x^{2} + 4 x \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06831, size = 24, normalized size = 1.41 \begin{align*} \frac{1}{4} \, \log \left ({\left | x^{3} + 2 \, x + 4 \right |}\right ) + \frac{1}{4} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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