Optimal. Leaf size=16 \[ \frac{1}{2 b \left (a+\frac{b}{x}\right )^2} \]
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Rubi [A] time = 0.0037841, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{1}{2 b \left (a+\frac{b}{x}\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x}\right )^3 x^2} \, dx &=\frac{1}{2 b \left (a+\frac{b}{x}\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0050624, size = 20, normalized size = 1.25 \[ -\frac{2 a x+b}{2 a^2 (a x+b)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 27, normalized size = 1.7 \begin{align*}{\frac{b}{2\,{a}^{2} \left ( ax+b \right ) ^{2}}}-{\frac{1}{{a}^{2} \left ( ax+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03062, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{2 \,{\left (a + \frac{b}{x}\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.68739, size = 68, normalized size = 4.25 \begin{align*} -\frac{2 \, a x + b}{2 \,{\left (a^{4} x^{2} + 2 \, a^{3} b x + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.32568, size = 32, normalized size = 2. \begin{align*} - \frac{2 a x + b}{2 a^{4} x^{2} + 4 a^{3} b x + 2 a^{2} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08913, size = 19, normalized size = 1.19 \begin{align*} \frac{1}{2 \,{\left (a + \frac{b}{x}\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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