Optimal. Leaf size=19 \[ -\frac {3 b}{7 x^{7/3}}-\frac {a}{2 x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, 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}{2 x^2}-\frac {3 b}{7 x^{7/3}} \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^3} \, dx &=\int \left (\frac {b}{x^{10/3}}+\frac {a}{x^3}\right ) \, dx\\ &=-\frac {3 b}{7 x^{7/3}}-\frac {a}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 1.11 \begin {gather*} \frac {-6 b-7 a \sqrt [3]{x}}{14 x^{7/3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(-\frac {3 b}{7 x^{\frac {7}{3}}}-\frac {a}{2 x^{2}}\) | \(14\) |
default | \(-\frac {3 b}{7 x^{\frac {7}{3}}}-\frac {a}{2 x^{2}}\) | \(14\) |
trager | \(\frac {\left (x -1\right ) a \left (x +1\right )}{2 x^{2}}-\frac {3 b}{7 x^{\frac {7}{3}}}\) | \(20\) |
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. 98 vs.
\(2 (13) = 26\).
time = 0.30, size = 98, normalized size = 5.16 \begin {gather*} -\frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7}}{7 \, b^{6}} + \frac {5 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a}{2 \, b^{6}} - \frac {6 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{2}}{b^{6}} + \frac {15 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{3}}{2 \, b^{6}} - \frac {5 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{3} a^{4}}{b^{6}} + \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{2} a^{5}}{2 \, b^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.84 \begin {gather*} -\frac {7 \, a x + 6 \, b x^{\frac {2}{3}}}{14 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 17, normalized size = 0.89 \begin {gather*} - \frac {a}{2 x^{2}} - \frac {3 b}{7 x^{\frac {7}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 15, normalized size = 0.79 \begin {gather*} -\frac {7 \, a x^{\frac {1}{3}} + 6 \, b}{14 \, x^{\frac {7}{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 = 0.68 \begin {gather*} -\frac {a}{2\,x^2}-\frac {3\,b}{7\,x^{7/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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