Optimal. Leaf size=21 \[ \frac {3}{2} a x^{2/3}+\frac {3}{5} b x^{5/3} \]
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Rubi [A] time = 0.00, antiderivative size = 21, 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*} \frac {3}{2} a x^{2/3}+\frac {3}{5} b x^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{\sqrt [3]{x}} \, dx &=\int \left (\frac {a}{\sqrt [3]{x}}+b x^{2/3}\right ) \, dx\\ &=\frac {3}{2} a x^{2/3}+\frac {3}{5} b x^{5/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {3}{10} x^{2/3} (5 a+2 b x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {3}{10} \left (5 a x^{2/3}+2 b x^{5/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.30, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{10} \, {\left (2 \, b x + 5 \, a\right )} x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{5} \, b x^{\frac {5}{3}} + \frac {3}{2} \, a 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 = 14, normalized size = 0.67 \begin {gather*} \frac {3 \left (2 b x +5 a \right ) x^{\frac {2}{3}}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{5} \, b x^{\frac {5}{3}} + \frac {3}{2} \, a x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.62 \begin {gather*} \frac {3\,x^{2/3}\,\left (5\,a+2\,b\,x\right )}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.66, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 a x^{\frac {2}{3}}}{2} + \frac {3 b x^{\frac {5}{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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