Optimal. Leaf size=13 \[ \frac {\sqrt {x^8+1}}{4} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {\sqrt {x^8+1}}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 9, normalized size = 0.69 \[ \frac {1}{4} \, \sqrt {x^{8} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.69 \[ \frac {1}{4} \, \sqrt {x^{8} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \[ \frac {\sqrt {x^{8}+1}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 9, normalized size = 0.69 \[ \frac {1}{4} \, \sqrt {x^{8} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 9, normalized size = 0.69 \[ \frac {\sqrt {x^8+1}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 8, normalized size = 0.62 \[ \frac {\sqrt {x^{8} + 1}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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