Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x}\right )^3}{3 b} \]
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Rubi [A] time = 0.0034732, 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} \[ -\frac{\left (a+\frac{b}{x}\right )^3}{3 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{x}\right )^2}{x^2} \, dx &=-\frac{\left (a+\frac{b}{x}\right )^3}{3 b}\\ \end{align*}
Mathematica [A] time = 0.0059557, size = 26, normalized size = 1.62 \[ -\frac{a^2}{x}-\frac{a b}{x^2}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 1.6 \begin{align*} -{\frac{{b}^{2}}{3\,{x}^{3}}}-{\frac{ab}{{x}^{2}}}-{\frac{{a}^{2}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957856, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{3}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.3659, size = 51, normalized size = 3.19 \begin{align*} -\frac{3 \, a^{2} x^{2} + 3 \, a b x + b^{2}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.290183, size = 24, normalized size = 1.5 \begin{align*} - \frac{3 a^{2} x^{2} + 3 a b x + b^{2}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15208, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{3}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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