Optimal. Leaf size=16 \[ \frac{1}{8} \left (x^4+4 x^2+1\right )^2 \]
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Rubi [A] time = 0.0066653, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {1588} \[ \frac{1}{8} \left (x^4+4 x^2+1\right )^2 \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \left (2 x+x^3\right ) \left (1+4 x^2+x^4\right ) \, dx &=\frac{1}{8} \left (1+4 x^2+x^4\right )^2\\ \end{align*}
Mathematica [A] time = 0.0014668, size = 21, normalized size = 1.31 \[ \frac{x^8}{8}+x^6+\frac{9 x^4}{4}+x^2 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 1.1 \begin{align*}{\frac{{x}^{8}}{8}}+{x}^{6}+{\frac{9\,{x}^{4}}{4}}+{x}^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.985187, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{8} \,{\left (x^{4} + 4 \, x^{2} + 1\right )}^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.10848, size = 42, normalized size = 2.62 \begin{align*} \frac{1}{8} x^{8} + x^{6} + \frac{9}{4} x^{4} + x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.053976, size = 17, normalized size = 1.06 \begin{align*} \frac{x^{8}}{8} + x^{6} + \frac{9 x^{4}}{4} + x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1962, size = 23, normalized size = 1.44 \begin{align*} \frac{1}{8} \, x^{8} + x^{6} + \frac{9}{4} \, x^{4} + x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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