Optimal. Leaf size=13 \[ -\frac {1}{\sqrt [3]{1-\frac {3}{x}}} \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {267}
\begin {gather*} -\frac {1}{\sqrt [3]{1-\frac {3}{x}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {1}{\left (1-\frac {3}{x}\right )^{4/3} x^2} \, dx &=-\frac {1}{\sqrt [3]{1-\frac {3}{x}}}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} -\frac {1}{\sqrt [3]{\frac {-3+x}{x}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 12, normalized size = 0.92
method | result | size |
derivativedivides | \(-\frac {1}{\left (1-\frac {3}{x}\right )^{\frac {1}{3}}}\) | \(12\) |
default | \(-\frac {1}{\left (1-\frac {3}{x}\right )^{\frac {1}{3}}}\) | \(12\) |
risch | \(-\frac {1}{\left (\frac {-3+x}{x}\right )^{\frac {1}{3}}}\) | \(12\) |
gosper | \(-\frac {-3+x}{x \left (\frac {-3+x}{x}\right )^{\frac {4}{3}}}\) | \(18\) |
trager | \(-\frac {x \left (-\frac {3-x}{x}\right )^{\frac {2}{3}}}{-3+x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.89, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{{\left (-\frac {3}{x} + 1\right )}^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.16, size = 17, normalized size = 1.31 \begin {gather*} -\frac {x \left (\frac {x - 3}{x}\right )^{\frac {2}{3}}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.25, size = 10, normalized size = 0.77 \begin {gather*} - \frac {1}{\sqrt [3]{1 - \frac {3}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.07, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{\left (\frac {x - 3}{x}\right )^{\frac {1}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.46, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{{\left (1-\frac {3}{x}\right )}^{1/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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