Optimal. Leaf size=21 \[ \frac {3}{7} a x^{7/3}+\frac {3}{10} b x^{10/3} \]
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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}{7} a x^{7/3}+\frac {3}{10} b x^{10/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^{4/3} (a+b x) \, dx &=\int \left (a x^{4/3}+b x^{7/3}\right ) \, dx\\ &=\frac {3}{7} a x^{7/3}+\frac {3}{10} b x^{10/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {3}{70} x^{7/3} (10 a+7 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}{70} \left (10 a x^{7/3}+7 b x^{10/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 18, normalized size = 0.86 \begin {gather*} \frac {3}{70} \, {\left (7 \, b x^{3} + 10 \, a x^{2}\right )} x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{10} \, b x^{\frac {10}{3}} + \frac {3}{7} \, a x^{\frac {7}{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 (7 b x +10 a \right ) x^{\frac {7}{3}}}{70} \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}{10} \, b x^{\frac {10}{3}} + \frac {3}{7} \, a x^{\frac {7}{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^{7/3}\,\left (10\,a+7\,b\,x\right )}{70} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.30, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 a x^{\frac {7}{3}}}{7} + \frac {3 b x^{\frac {10}{3}}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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