Optimal. Leaf size=16 \[ -\frac {\left (x^6+1\right )^{3/2}}{9 x^9} \]
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Rubi [A] time = 0.00, antiderivative size = 16, 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 = {264} \begin {gather*} -\frac {\left (x^6+1\right )^{3/2}}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx &=-\frac {\left (1+x^6\right )^{3/2}}{9 x^9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (x^6+1\right )^{3/2}}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.12, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (1+x^6\right )^{3/2}}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 16, normalized size = 1.00 \begin {gather*} -\frac {x^{9} + {\left (x^{6} + 1\right )}^{\frac {3}{2}}}{9 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 18, normalized size = 1.12 \begin {gather*} -\frac {{\left (\frac {1}{x^{6}} + 1\right )}^{\frac {3}{2}}}{9 \, \mathrm {sgn}\relax (x)} + \frac {1}{9} \, \mathrm {sgn}\relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 13, normalized size = 0.81
method | result | size |
trager | \(-\frac {\left (x^{6}+1\right )^{\frac {3}{2}}}{9 x^{9}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{6}+1\right )^{\frac {3}{2}}}{9 x^{9}}\) | \(13\) |
risch | \(-\frac {x^{12}+2 x^{6}+1}{9 x^{9} \sqrt {x^{6}+1}}\) | \(23\) |
gosper | \(-\frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right ) \sqrt {x^{6}+1}}{9 x^{9}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{6} + 1\right )}^{\frac {3}{2}}}{9 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^6+1\right )}^{3/2}}{9\,x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.79, size = 27, normalized size = 1.69 \begin {gather*} - \frac {\sqrt {1 + \frac {1}{x^{6}}}}{9} - \frac {\sqrt {1 + \frac {1}{x^{6}}}}{9 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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