Optimal. Leaf size=14 \[ -\frac{3}{b \sqrt [3]{a+b x}} \]
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Rubi [A] time = 0.0013637, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ -\frac{3}{b \sqrt [3]{a+b x}} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^{4/3}} \, dx &=-\frac{3}{b \sqrt [3]{a+b x}}\\ \end{align*}
Mathematica [A] time = 0.0122369, size = 14, normalized size = 1. \[ -\frac{3}{b \sqrt [3]{a+b x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*} -3\,{\frac{1}{b\sqrt [3]{bx+a}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01713, size = 16, normalized size = 1.14 \begin{align*} -\frac{3}{{\left (b x + a\right )}^{\frac{1}{3}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44181, size = 46, normalized size = 3.29 \begin{align*} -\frac{3 \,{\left (b x + a\right )}^{\frac{2}{3}}}{b^{2} x + a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.107064, size = 12, normalized size = 0.86 \begin{align*} - \frac{3}{b \sqrt [3]{a + b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20436, size = 16, normalized size = 1.14 \begin{align*} -\frac{3}{{\left (b x + a\right )}^{\frac{1}{3}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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