Optimal. Leaf size=17 \[ -\frac {3 b}{4 x^{4/3}}-\frac {a}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14}
\begin {gather*} -\frac {a}{x}-\frac {3 b}{4 x^{4/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^2} \, dx &=\int \left (\frac {b}{x^{7/3}}+\frac {a}{x^2}\right ) \, dx\\ &=-\frac {3 b}{4 x^{4/3}}-\frac {a}{x}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 1.00 \begin {gather*} -\frac {3 b}{4 x^{4/3}}-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.82
method | result | size |
derivativedivides | \(-\frac {3 b}{4 x^{\frac {4}{3}}}-\frac {a}{x}\) | \(14\) |
default | \(-\frac {3 b}{4 x^{\frac {4}{3}}}-\frac {a}{x}\) | \(14\) |
trager | \(\frac {a \left (x -1\right )}{x}-\frac {3 b}{4 x^{\frac {4}{3}}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 47 vs.
\(2 (13) = 26\).
time = 0.31, size = 47, normalized size = 2.76 \begin {gather*} -\frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4}}{4 \, b^{3}} + \frac {2 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{3} a}{b^{3}} - \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{2} a^{2}}{2 \, b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 16, normalized size = 0.94 \begin {gather*} -\frac {4 \, a x + 3 \, b x^{\frac {2}{3}}}{4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.21, size = 14, normalized size = 0.82 \begin {gather*} - \frac {a}{x} - \frac {3 b}{4 x^{\frac {4}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, size = 15, normalized size = 0.88 \begin {gather*} -\frac {4 \, a x^{\frac {1}{3}} + 3 \, b}{4 \, x^{\frac {4}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.13, size = 13, normalized size = 0.76 \begin {gather*} -\frac {a}{x}-\frac {3\,b}{4\,x^{4/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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