Optimal. Leaf size=19 \[ 3 b \sqrt [3]{x}-\frac {3 a}{2 x^{2/3}} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} 3 b \sqrt [3]{x}-\frac {3 a}{2 x^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{5/3}} \, dx &=\int \left (\frac {a}{x^{5/3}}+\frac {b}{x^{2/3}}\right ) \, dx\\ &=-\frac {3 a}{2 x^{2/3}}+3 b \sqrt [3]{x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} 3 b \sqrt [3]{x}-\frac {3 a}{2 x^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} \frac {3 (2 b x-a)}{2 x^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 13, normalized size = 0.68 \begin {gather*} \frac {3 \, {\left (2 \, b x - a\right )}}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 13, normalized size = 0.68 \begin {gather*} 3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} -\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 13, normalized size = 0.68 \begin {gather*} 3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} -\frac {3\,a-6\,b\,x}{2\,x^{2/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 17, normalized size = 0.89 \begin {gather*} - \frac {3 a}{2 x^{\frac {2}{3}}} + 3 b \sqrt [3]{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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