Optimal. Leaf size=19 \[ \frac{3}{2} b x^{2/3}-\frac{3 a}{\sqrt [3]{x}} \]
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Rubi [A] time = 0.0036323, antiderivative size = 19, normalized size of antiderivative = 1., 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} \[ \frac{3}{2} b x^{2/3}-\frac{3 a}{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^{4/3}} \, dx &=\int \left (\frac{a}{x^{4/3}}+\frac{b}{\sqrt [3]{x}}\right ) \, dx\\ &=-\frac{3 a}{\sqrt [3]{x}}+\frac{3}{2} b x^{2/3}\\ \end{align*}
Mathematica [A] time = 0.0051168, size = 16, normalized size = 0.84 \[ \frac{3 (b x-2 a)}{2 \sqrt [3]{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \begin{align*} -{\frac{-3\,bx+6\,a}{2}{\frac{1}{\sqrt [3]{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07173, size = 18, normalized size = 0.95 \begin{align*} \frac{3}{2} \, b x^{\frac{2}{3}} - \frac{3 \, a}{x^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53729, size = 34, normalized size = 1.79 \begin{align*} \frac{3 \,{\left (b x - 2 \, a\right )}}{2 \, x^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.437249, size = 17, normalized size = 0.89 \begin{align*} - \frac{3 a}{\sqrt [3]{x}} + \frac{3 b x^{\frac{2}{3}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06447, size = 18, normalized size = 0.95 \begin{align*} \frac{3}{2} \, b x^{\frac{2}{3}} - \frac{3 \, a}{x^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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