Optimal. Leaf size=13 \[ \frac{\sqrt{x^8+1}}{4} \]
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Rubi [A] time = 0.0025551, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{\sqrt{x^8+1}}{4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^7}{\sqrt{1+x^8}} \, dx &=\frac{\sqrt{1+x^8}}{4}\\ \end{align*}
Mathematica [A] time = 0.001798, size = 13, normalized size = 1. \[ \frac{\sqrt{x^8+1}}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{4}\sqrt{{x}^{8}+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955257, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{4} \, \sqrt{x^{8} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24983, size = 26, normalized size = 2. \begin{align*} \frac{1}{4} \, \sqrt{x^{8} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.417179, size = 8, normalized size = 0.62 \begin{align*} \frac{\sqrt{x^{8} + 1}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14609, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{4} \, \sqrt{x^{8} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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