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 = 0.0106383, antiderivative size = 30, normalized size of antiderivative = 1., 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 263
Rule 43
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*}
Mathematica [A] time = 0.003243, size = 30, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{b}^{2}}{6\,{x}^{6}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{a}^{2}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989748, size = 32, normalized size = 1.07 \begin{align*} -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41486, size = 59, normalized size = 1.97 \begin{align*} -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.329647, size = 26, normalized size = 0.87 \begin{align*} - \frac{15 a^{2} x^{2} + 24 a b x + 10 b^{2}}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16572, size = 32, normalized size = 1.07 \begin{align*} -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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