Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]
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Rubi [A] time = 0.0047732, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {14} \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+\frac{b}{x}}{x^5} \, dx &=\int \left (\frac{b}{x^6}+\frac{a}{x^5}\right ) \, dx\\ &=-\frac{b}{5 x^5}-\frac{a}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0017936, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{b}{5\,{x}^{5}}}-{\frac{a}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949941, size = 18, normalized size = 1.06 \begin{align*} -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41887, size = 34, normalized size = 2. \begin{align*} -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.265212, size = 14, normalized size = 0.82 \begin{align*} - \frac{5 a x + 4 b}{20 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20837, size = 18, normalized size = 1.06 \begin{align*} -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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