Optimal. Leaf size=16 \[ -\frac {\left (1+x^6\right )^{2/3}}{4 x^4} \]
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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 = {270}
\begin {gather*} -\frac {\left (x^6+1\right )^{2/3}}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {1}{x^5 \sqrt [3]{1+x^6}} \, dx &=-\frac {\left (1+x^6\right )^{2/3}}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.48, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (1+x^6\right )^{2/3}}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 13, normalized size = 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 | \(-\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{4}}\) | \(13\) |
gosper | \(-\frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right )}{4 x^{4} \left (x^{6}+1\right )^{\frac {1}{3}}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{6} + 1\right )}^{\frac {2}{3}}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{6} + 1\right )}^{\frac {2}{3}}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.37, size = 22, normalized size = 1.38 \begin {gather*} \frac {\left (1 + \frac {1}{x^{6}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {2}{3}\right )}{6 \Gamma \left (\frac {1}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^6+1\right )}^{2/3}}{4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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