Optimal. Leaf size=17 \[ \frac {1}{4} \log \left (x^4+2 x^2+4 x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.80, size = 15, normalized size = 0.88 \[ \frac {1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 18, normalized size = 1.06 \[ \frac {1}{4} \, \log \left (4 \, {\left | \frac {1}{4} \, x^{4} + \frac {1}{2} \, x^{2} + x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {\ln \left (\left (x^{3}+2 x +4\right ) x \right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 15, normalized size = 0.88 \[ \frac {1}{4} \, \log \left (x^{4} + 2 \, x^{2} + 4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 13, normalized size = 0.76 \[ \frac {\ln \left (x\,\left (x^3+2\,x+4\right )\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.82 \[ \frac {\log {\left (x^{4} + 2 x^{2} + 4 x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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