Optimal. Leaf size=14 \[ \frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \]
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Rubi [A]
time = 0.00, antiderivative size = 14, 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*} \frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx &=\frac {\int x^2 \, dx}{\left (\frac {b}{x^3}\right )^{2/3} x^2}\\ &=\frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.79
method | result | size |
gosper | \(\frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}}\) | \(11\) |
risch | \(\frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}}\) | \(11\) |
trager | \(\frac {x \left (x^{2}+x +1\right ) \left (x -1\right ) \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}}{3 b}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 10, normalized size = 0.71 \begin {gather*} \frac {x}{3 \, \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 15, normalized size = 1.07 \begin {gather*} \frac {x^{4} \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 10, normalized size = 0.71 \begin {gather*} \frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.15, size = 10, normalized size = 0.71 \begin {gather*} \frac {x}{3 \, \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.90, size = 15, normalized size = 1.07 \begin {gather*} \frac {x^4\,{\left (\frac {b}{x^3}\right )}^{1/3}}{3\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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