Optimal. Leaf size=21 \[ \frac {3}{5} a x^{5/3}+\frac {3}{8} b x^{8/3} \]
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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}{5} a x^{5/3}+\frac {3}{8} b x^{8/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^{2/3} (a+b x) \, dx &=\int \left (a x^{2/3}+b x^{5/3}\right ) \, dx\\ &=\frac {3}{5} a x^{5/3}+\frac {3}{8} b x^{8/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {3}{40} x^{5/3} (8 a+5 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}{40} \left (8 a x^{5/3}+5 b x^{8/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 16, normalized size = 0.76 \begin {gather*} \frac {3}{40} \, {\left (5 \, b x^{2} + 8 \, a x\right )} x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{8} \, b x^{\frac {8}{3}} + \frac {3}{5} \, a x^{\frac {5}{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 (5 b x +8 a \right ) x^{\frac {5}{3}}}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{8} \, b x^{\frac {8}{3}} + \frac {3}{5} \, a x^{\frac {5}{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^{5/3}\,\left (8\,a+5\,b\,x\right )}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 a x^{\frac {5}{3}}}{5} + \frac {3 b x^{\frac {8}{3}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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