Optimal. Leaf size=19 \[ -\frac {3 b}{10 x^{10/3}}-\frac {a}{3 x^3} \]
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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}{3 x^3}-\frac {3 b}{10 x^{10/3}} \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^4} \, dx &=\int \left (\frac {b}{x^{13/3}}+\frac {a}{x^4}\right ) \, dx\\ &=-\frac {3 b}{10 x^{10/3}}-\frac {a}{3 x^3}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 1.11 \begin {gather*} \frac {-9 b-10 a \sqrt [3]{x}}{30 x^{10/3}} \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 | \(-\frac {3 b}{10 x^{\frac {10}{3}}}-\frac {a}{3 x^{3}}\) | \(14\) |
default | \(-\frac {3 b}{10 x^{\frac {10}{3}}}-\frac {a}{3 x^{3}}\) | \(14\) |
trager | \(\frac {a \left (x^{2}+x +1\right ) \left (x -1\right )}{3 x^{3}}-\frac {3 b}{10 x^{\frac {10}{3}}}\) | \(23\) |
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. 149 vs.
\(2 (13) = 26\).
time = 0.29, size = 149, normalized size = 7.84 \begin {gather*} -\frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{10}}{10 \, b^{9}} + \frac {8 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{9} a}{3 \, b^{9}} - \frac {21 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{8} a^{2}}{2 \, b^{9}} + \frac {24 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7} a^{3}}{b^{9}} - \frac {35 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a^{4}}{b^{9}} + \frac {168 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{5}}{5 \, b^{9}} - \frac {21 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{6}}{b^{9}} + \frac {8 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{3} a^{7}}{b^{9}} - \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{2} a^{8}}{2 \, b^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 16, normalized size = 0.84 \begin {gather*} -\frac {10 \, a x + 9 \, b x^{\frac {2}{3}}}{30 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.43, size = 17, normalized size = 0.89 \begin {gather*} - \frac {a}{3 x^{3}} - \frac {3 b}{10 x^{\frac {10}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 15, normalized size = 0.79 \begin {gather*} -\frac {10 \, a x^{\frac {1}{3}} + 9 \, b}{30 \, x^{\frac {10}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.11, size = 13, normalized size = 0.68 \begin {gather*} -\frac {a}{3\,x^3}-\frac {3\,b}{10\,x^{10/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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