Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x}\right )^4}{4 b} \]
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Rubi [A] time = 0.0034446, 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} \[ -\frac{\left (a+\frac{b}{x}\right )^4}{4 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{x}\right )^3}{x^2} \, dx &=-\frac{\left (a+\frac{b}{x}\right )^4}{4 b}\\ \end{align*}
Mathematica [B] time = 0.0033146, size = 39, normalized size = 2.44 \[ -\frac{3 a^2 b}{2 x^2}-\frac{a^3}{x}-\frac{a b^2}{x^3}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 36, normalized size = 2.3 \begin{align*} -{\frac{{b}^{2}a}{{x}^{3}}}-{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{3\,{a}^{2}b}{2\,{x}^{2}}}-{\frac{{a}^{3}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963718, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{4}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.42868, size = 73, normalized size = 4.56 \begin{align*} -\frac{4 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a b^{2} x + b^{3}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.344411, size = 36, normalized size = 2.25 \begin{align*} - \frac{4 a^{3} x^{3} + 6 a^{2} b x^{2} + 4 a b^{2} x + b^{3}}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16773, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{4}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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