Optimal. Leaf size=17 \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]
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Rubi [A] time = 0.004701, 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} \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+\frac{b}{x}}{x^6} \, dx &=\int \left (\frac{b}{x^7}+\frac{a}{x^6}\right ) \, dx\\ &=-\frac{b}{6 x^6}-\frac{a}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0015256, size = 17, normalized size = 1. \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{b}{6\,{x}^{6}}}-{\frac{a}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952965, size = 18, normalized size = 1.06 \begin{align*} -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35814, size = 34, normalized size = 2. \begin{align*} -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.271038, size = 14, normalized size = 0.82 \begin{align*} - \frac{6 a x + 5 b}{30 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17312, size = 18, normalized size = 1.06 \begin{align*} -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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