Optimal. Leaf size=30 \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{5 x^5}-\frac {b^2}{6 x^6} \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {263, 43} \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{5 x^5}-\frac {b^2}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{x}\right )^2}{x^5} \, dx &=\int \frac {(b+a x)^2}{x^7} \, dx\\ &=\int \left (\frac {b^2}{x^7}+\frac {2 a b}{x^6}+\frac {a^2}{x^5}\right ) \, dx\\ &=-\frac {b^2}{6 x^6}-\frac {2 a b}{5 x^5}-\frac {a^2}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{5 x^5}-\frac {b^2}{6 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 24, normalized size = 0.80 \[ -\frac {15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.80 \[ -\frac {15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \[ -\frac {a^{2}}{4 x^{4}}-\frac {2 a b}{5 x^{5}}-\frac {b^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.96, size = 24, normalized size = 0.80 \[ -\frac {15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 24, normalized size = 0.80 \[ -\frac {\frac {a^2\,x^2}{4}+\frac {2\,a\,b\,x}{5}+\frac {b^2}{6}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 26, normalized size = 0.87 \[ \frac {- 15 a^{2} x^{2} - 24 a b x - 10 b^{2}}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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