Optimal. Leaf size=12 \[ -3 x \left (\frac {b}{x^2}\right )^{2/3} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ -3 x \left (\frac {b}{x^2}\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (\frac {b}{x^2}\right )^{2/3} \, dx &=\left (\left (\frac {b}{x^2}\right )^{2/3} x^{4/3}\right ) \int \frac {1}{x^{4/3}} \, dx\\ &=-3 \left (\frac {b}{x^2}\right )^{2/3} x\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ -3 x \left (\frac {b}{x^2}\right )^{2/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 10, normalized size = 0.83 \[ -3 \, x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
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 \[ \int \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \[ -3 \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 10, normalized size = 0.83 \[ -3 \, x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 11, normalized size = 0.92 \[ -3\,b^{2/3}\,x\,{\left (\frac {1}{x^2}\right )}^{2/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 17, normalized size = 1.42 \[ - 3 b^{\frac {2}{3}} x \left (\frac {1}{x^{2}}\right )^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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