Integrand size = 13, antiderivative size = 16 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {\left (1+x^6\right )^{2/3}}{4 x^4} \]
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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} \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {\left (x^6+1\right )^{2/3}}{4 x^4} \]
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Rule 270
Rubi steps \begin{align*} \text {integral}& = -\frac {\left (1+x^6\right )^{2/3}}{4 x^4} \\ \end{align*}
Time = 0.57 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {\left (1+x^6\right )^{2/3}}{4 x^4} \]
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Time = 0.78 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81
method | result | size |
trager | \(-\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{4}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{4}}\) | \(13\) |
risch | \(-\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{4}}\) | \(13\) |
pseudoelliptic | \(-\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{4}}\) | \(13\) |
gosper | \(-\frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right )}{4 x^{4} \left (x^{6}+1\right )^{\frac {1}{3}}}\) | \(28\) |
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Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {{\left (x^{6} + 1\right )}^{\frac {2}{3}}}{4 \, x^{4}} \]
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Time = 0.35 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=\frac {\left (1 + \frac {1}{x^{6}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {2}{3}\right )}{6 \Gamma \left (\frac {1}{3}\right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {{\left (x^{6} + 1\right )}^{\frac {2}{3}}}{4 \, x^{4}} \]
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\[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=\int { \frac {1}{{\left (x^{6} + 1\right )}^{\frac {1}{3}} x^{5}} \,d x } \]
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Time = 4.95 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx=-\frac {{\left (x^6+1\right )}^{2/3}}{4\,x^4} \]
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