Optimal. Leaf size=19 \[ 3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3} \]
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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} \[ 3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{2/3}} \, dx &=\int \left (\frac {a}{x^{2/3}}+b \sqrt [3]{x}\right ) \, dx\\ &=3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.84 \[ \frac {3}{4} \sqrt [3]{x} (4 a+b x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 0.63 \[ \frac {3}{4} \, {\left (b x + 4 \, a\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 13, normalized size = 0.68 \[ \frac {3}{4} \, b x^{\frac {4}{3}} + 3 \, a x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.68 \[ \frac {3 \left (b x +4 a \right ) x^{\frac {1}{3}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 13, normalized size = 0.68 \[ \frac {3}{4} \, b x^{\frac {4}{3}} + 3 \, a x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.63 \[ \frac {3\,x^{1/3}\,\left (4\,a+b\,x\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.49, size = 17, normalized size = 0.89 \[ 3 a \sqrt [3]{x} + \frac {3 b x^{\frac {4}{3}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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