Optimal. Leaf size=11 \[ \frac{1}{24} \left (x^2+1\right )^{12} \]
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Rubi [A] time = 0.0023995, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {28, 261} \[ \frac{1}{24} \left (x^2+1\right )^{12} \]
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin{align*} \int x \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx &=\int x \left (1+x^2\right )^{11} \, dx\\ &=\frac{1}{24} \left (1+x^2\right )^{12}\\ \end{align*}
Mathematica [A] time = 0.0017517, size = 11, normalized size = 1. \[ \frac{1}{24} \left (x^2+1\right )^{12} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 62, normalized size = 5.6 \begin{align*}{\frac{{x}^{24}}{24}}+{\frac{{x}^{22}}{2}}+{\frac{11\,{x}^{20}}{4}}+{\frac{55\,{x}^{18}}{6}}+{\frac{165\,{x}^{16}}{8}}+33\,{x}^{14}+{\frac{77\,{x}^{12}}{2}}+33\,{x}^{10}+{\frac{165\,{x}^{8}}{8}}+{\frac{55\,{x}^{6}}{6}}+{\frac{11\,{x}^{4}}{4}}+{\frac{{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.981964, size = 82, normalized size = 7.45 \begin{align*} \frac{1}{24} \, x^{24} + \frac{1}{2} \, x^{22} + \frac{11}{4} \, x^{20} + \frac{55}{6} \, x^{18} + \frac{165}{8} \, x^{16} + 33 \, x^{14} + \frac{77}{2} \, x^{12} + 33 \, x^{10} + \frac{165}{8} \, x^{8} + \frac{55}{6} \, x^{6} + \frac{11}{4} \, x^{4} + \frac{1}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.46461, size = 182, normalized size = 16.55 \begin{align*} \frac{1}{24} x^{24} + \frac{1}{2} x^{22} + \frac{11}{4} x^{20} + \frac{55}{6} x^{18} + \frac{165}{8} x^{16} + 33 x^{14} + \frac{77}{2} x^{12} + 33 x^{10} + \frac{165}{8} x^{8} + \frac{55}{6} x^{6} + \frac{11}{4} x^{4} + \frac{1}{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.068124, size = 71, normalized size = 6.45 \begin{align*} \frac{x^{24}}{24} + \frac{x^{22}}{2} + \frac{11 x^{20}}{4} + \frac{55 x^{18}}{6} + \frac{165 x^{16}}{8} + 33 x^{14} + \frac{77 x^{12}}{2} + 33 x^{10} + \frac{165 x^{8}}{8} + \frac{55 x^{6}}{6} + \frac{11 x^{4}}{4} + \frac{x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11146, size = 82, normalized size = 7.45 \begin{align*} \frac{1}{24} \, x^{24} + \frac{1}{2} \, x^{22} + \frac{11}{4} \, x^{20} + \frac{55}{6} \, x^{18} + \frac{165}{8} \, x^{16} + 33 \, x^{14} + \frac{77}{2} \, x^{12} + 33 \, x^{10} + \frac{165}{8} \, x^{8} + \frac{55}{6} \, x^{6} + \frac{11}{4} \, x^{4} + \frac{1}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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