Optimal. Leaf size=14 \[ -\frac{1}{2 a (a x+b)^2} \]
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Rubi [A] time = 0.0037481, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 32} \[ -\frac{1}{2 a (a x+b)^2} \]
Antiderivative was successfully verified.
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Rule 263
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x}\right )^3 x^3} \, dx &=\int \frac{1}{(b+a x)^3} \, dx\\ &=-\frac{1}{2 a (b+a x)^2}\\ \end{align*}
Mathematica [A] time = 0.0024803, size = 14, normalized size = 1. \[ -\frac{1}{2 a (a x+b)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,a \left ( ax+b \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961641, size = 32, normalized size = 2.29 \begin{align*} -\frac{1}{2 \,{\left (a^{3} x^{2} + 2 \, a^{2} b x + a b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64829, size = 49, normalized size = 3.5 \begin{align*} -\frac{1}{2 \,{\left (a^{3} x^{2} + 2 \, a^{2} b x + a b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.316896, size = 26, normalized size = 1.86 \begin{align*} - \frac{1}{2 a^{3} x^{2} + 4 a^{2} b x + 2 a b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13612, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{2 \,{\left (a x + b\right )}^{2} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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