Optimal. Leaf size=16 \[ -\frac {\left (a+\frac {b}{x}\right )^3}{3 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.93, size = 22, normalized size = 1.38 \[ -\frac {3 \, a^{2} x^{2} + 3 \, a b x + b^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{3}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 1.56 \[ -\frac {a^{2}}{x}-\frac {a b}{x^{2}}-\frac {b^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{3}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 22, normalized size = 1.38 \[ -\frac {a^2\,x^2+a\,b\,x+\frac {b^2}{3}}{x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 24, normalized size = 1.50 \[ \frac {- 3 a^{2} x^{2} - 3 a b x - b^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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