Optimal. Leaf size=12 \[ -3 \sqrt [3]{\frac {b}{x^4}} x \]
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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}
\begin {gather*} -3 x \sqrt [3]{\frac {b}{x^4}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \sqrt [3]{\frac {b}{x^4}} \, dx &=\left (\sqrt [3]{\frac {b}{x^4}} x^{4/3}\right ) \int \frac {1}{x^{4/3}} \, dx\\ &=-3 \sqrt [3]{\frac {b}{x^4}} x\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -3 \sqrt [3]{\frac {b}{x^4}} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 11, normalized size = 0.92
method | result | size |
gosper | \(-3 \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} x\) | \(11\) |
trager | \(-3 \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} x\) | \(11\) |
risch | \(-3 \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} x\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 10, normalized size = 0.83 \begin {gather*} -3 \, x \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 10, normalized size = 0.83 \begin {gather*} -3 \, x \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 12, normalized size = 1.00 \begin {gather*} - 3 x \sqrt [3]{\frac {b}{x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 10, normalized size = 0.83 \begin {gather*} -3 \, x \left (\frac {b}{x^{4}}\right )^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.02, size = 11, normalized size = 0.92 \begin {gather*} -3\,b^{1/3}\,x\,{\left (\frac {1}{x^4}\right )}^{1/3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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