Optimal. Leaf size=13 \[ -\frac{1}{4 \left (x^4+x^2\right )^2} \]
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Rubi [A] time = 0.0070267, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {1588} \[ -\frac{1}{4 \left (x^4+x^2\right )^2} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{x+2 x^3}{\left (x^2+x^4\right )^3} \, dx &=-\frac{1}{4 \left (x^2+x^4\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0065667, size = 14, normalized size = 1.08 \[ -\frac{1}{4 x^4 \left (x^2+1\right )^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.01, size = 30, normalized size = 2.3 \begin{align*} -{\frac{1}{4\, \left ({x}^{2}+1 \right ) ^{2}}}-{\frac{1}{2\,{x}^{2}+2}}-{\frac{1}{4\,{x}^{4}}}+{\frac{1}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967609, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{4 \,{\left (x^{4} + x^{2}\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.937095, size = 35, normalized size = 2.69 \begin{align*} -\frac{1}{4 \,{\left (x^{8} + 2 \, x^{6} + x^{4}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.130826, size = 17, normalized size = 1.31 \begin{align*} - \frac{1}{4 x^{8} + 8 x^{6} + 4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20607, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{4 \,{\left (x^{4} + x^{2}\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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