Integrand size = 13, antiderivative size = 16 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {\left (1+x^6\right )^{3/2}}{9 x^9} \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {\left (x^6+1\right )^{3/2}}{9 x^9} \]
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Rule 270
Rubi steps \begin{align*} \text {integral}& = -\frac {\left (1+x^6\right )^{3/2}}{9 x^9} \\ \end{align*}
Time = 0.12 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {\left (1+x^6\right )^{3/2}}{9 x^9} \]
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Time = 0.75 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81
method | result | size |
trager | \(-\frac {\left (x^{6}+1\right )^{\frac {3}{2}}}{9 x^{9}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{6}+1\right )^{\frac {3}{2}}}{9 x^{9}}\) | \(13\) |
pseudoelliptic | \(-\frac {\left (x^{6}+1\right )^{\frac {3}{2}}}{9 x^{9}}\) | \(13\) |
risch | \(-\frac {x^{12}+2 x^{6}+1}{9 x^{9} \sqrt {x^{6}+1}}\) | \(23\) |
gosper | \(-\frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right ) \sqrt {x^{6}+1}}{9 x^{9}}\) | \(28\) |
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none
Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {x^{9} + {\left (x^{6} + 1\right )}^{\frac {3}{2}}}{9 \, x^{9}} \]
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Time = 0.47 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.69 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=- \frac {\sqrt {1 + \frac {1}{x^{6}}}}{9} - \frac {\sqrt {1 + \frac {1}{x^{6}}}}{9 x^{6}} \]
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none
Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {{\left (x^{6} + 1\right )}^{\frac {3}{2}}}{9 \, x^{9}} \]
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none
Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {{\left (\frac {1}{x^{6}} + 1\right )}^{\frac {3}{2}}}{9 \, \mathrm {sgn}\left (x\right )} + \frac {1}{9} \, \mathrm {sgn}\left (x\right ) \]
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Time = 5.58 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {\sqrt {1+x^6}}{x^{10}} \, dx=-\frac {{\left (x^6+1\right )}^{3/2}}{9\,x^9} \]
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