Optimal. Leaf size=13 \[ -\frac {3}{16} \left (\frac {1}{x^2}+1\right )^{8/3} \]
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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} \[ -\frac {3}{16} \left (\frac {1}{x^2}+1\right )^{8/3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {\left (1+\frac {1}{x^2}\right )^{5/3}}{x^3} \, dx &=-\frac {3}{16} \left (1+\frac {1}{x^2}\right )^{8/3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.62 \[ -\frac {3 \left (\frac {1}{x^2}+1\right )^{5/3} \left (x^2+1\right )}{16 x^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 26, normalized size = 2.00 \[ -\frac {3 \, {\left (x^{4} + 2 \, x^{2} + 1\right )} \left (\frac {x^{2} + 1}{x^{2}}\right )^{\frac {2}{3}}}{16 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.17, size = 23, normalized size = 1.77 \[ -\frac {3 \, {\left (x^{2} + 1\right )}^{2} \left (\frac {x^{2} + 1}{x^{2}}\right )^{\frac {2}{3}}}{16 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 22, normalized size = 1.69 \[ -\frac {3 \left (x^{2}+1\right ) \left (\frac {x^{2}+1}{x^{2}}\right )^{\frac {5}{3}}}{16 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 9, normalized size = 0.69 \[ -\frac {3}{16} \, {\left (\frac {1}{x^{2}} + 1\right )}^{\frac {8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.42, size = 19, normalized size = 1.46 \[ -\frac {3\,{\left (\frac {1}{x^2}+1\right )}^{2/3}\,{\left (x^2+1\right )}^2}{16\,x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.29, size = 48, normalized size = 3.69 \[ - \frac {3 \left (1 + \frac {1}{x^{2}}\right )^{\frac {2}{3}}}{16} - \frac {3 \left (1 + \frac {1}{x^{2}}\right )^{\frac {2}{3}}}{8 x^{2}} - \frac {3 \left (1 + \frac {1}{x^{2}}\right )^{\frac {2}{3}}}{16 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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