Optimal. Leaf size=21 \[ \frac {3}{4} a x^{4/3}+\frac {3}{7} b x^{7/3} \]
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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} \[ \frac {3}{4} a x^{4/3}+\frac {3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \sqrt [3]{x} (a+b x) \, dx &=\int \left (a \sqrt [3]{x}+b x^{4/3}\right ) \, dx\\ &=\frac {3}{4} a x^{4/3}+\frac {3}{7} b x^{7/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \[ \frac {3}{28} x^{4/3} (7 a+4 b x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 16, normalized size = 0.76 \[ \frac {3}{28} \, {\left (4 \, b x^{2} + 7 \, a x\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 13, normalized size = 0.62 \[ \frac {3}{7} \, b x^{\frac {7}{3}} + \frac {3}{4} \, a x^{\frac {4}{3}} \]
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 \[ \frac {3 \left (4 b x +7 a \right ) x^{\frac {4}{3}}}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 13, normalized size = 0.62 \[ \frac {3}{7} \, b x^{\frac {7}{3}} + \frac {3}{4} \, a x^{\frac {4}{3}} \]
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 \[ \frac {3\,x^{4/3}\,\left (7\,a+4\,b\,x\right )}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.52, size = 19, normalized size = 0.90 \[ \frac {3 a x^{\frac {4}{3}}}{4} + \frac {3 b x^{\frac {7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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