Optimal. Leaf size=22 \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]
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Rubi [A] time = 0.0026291, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (\frac{1}{x^5}+x+x^5\right ) \, dx &=-\frac{1}{4 x^4}+\frac{x^2}{2}+\frac{x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0012878, size = 22, normalized size = 1. \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 17, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{4}}}+{\frac{{x}^{2}}{2}}+{\frac{{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0322, size = 22, normalized size = 1. \begin{align*} \frac{1}{6} \, x^{6} + \frac{1}{2} \, x^{2} - \frac{1}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8937, size = 42, normalized size = 1.91 \begin{align*} \frac{2 \, x^{10} + 6 \, x^{6} - 3}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077435, size = 15, normalized size = 0.68 \begin{align*} \frac{x^{6}}{6} + \frac{x^{2}}{2} - \frac{1}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05989, size = 22, normalized size = 1. \begin{align*} \frac{1}{6} \, x^{6} + \frac{1}{2} \, x^{2} - \frac{1}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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