Optimal. Leaf size=16 \[ -\frac {\left (a+\frac {b}{x}\right )^4}{4 b} \]
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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} \[ -\frac {\left (a+\frac {b}{x}\right )^4}{4 b} \]
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*}
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Mathematica [B] time = 0.01, size = 39, normalized size = 2.44 \[ -\frac {a^3}{x}-\frac {3 a^2 b}{2 x^2}-\frac {a b^2}{x^3}-\frac {b^3}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 1.07, size = 33, normalized size = 2.06 \[ -\frac {4 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a b^{2} x + b^{3}}{4 \, x^{4}} \]
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 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{4}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 36, normalized size = 2.25 \[ -\frac {a^{3}}{x}-\frac {3 a^{2} b}{2 x^{2}}-\frac {a \,b^{2}}{x^{3}}-\frac {b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{4}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 33, normalized size = 2.06 \[ -\frac {a^3\,x^3+\frac {3\,a^2\,b\,x^2}{2}+a\,b^2\,x+\frac {b^3}{4}}{x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.22, size = 36, normalized size = 2.25 \[ \frac {- 4 a^{3} x^{3} - 6 a^{2} b x^{2} - 4 a b^{2} x - b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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