Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]
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Rubi [A] time = 0.0047952, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^5} \, dx &=\int \left (\frac{a}{x^5}+\frac{b}{x^4}\right ) \, dx\\ &=-\frac{a}{4 x^4}-\frac{b}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0021174, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{4\,{x}^{4}}}-{\frac{b}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01408, size = 18, normalized size = 1.06 \begin{align*} -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36441, size = 34, normalized size = 2. \begin{align*} -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.354097, size = 14, normalized size = 0.82 \begin{align*} - \frac{3 a + 4 b x}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.212, size = 18, normalized size = 1.06 \begin{align*} -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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