Optimal. Leaf size=17 \[ -\frac{a}{3 x^3}-\frac{b}{4 x^4} \]
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Rubi [A] time = 0.0048105, 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} \[ -\frac{a}{3 x^3}-\frac{b}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+\frac{b}{x}}{x^4} \, dx &=\int \left (\frac{b}{x^5}+\frac{a}{x^4}\right ) \, dx\\ &=-\frac{b}{4 x^4}-\frac{a}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0015422, size = 17, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{b}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{b}{4\,{x}^{4}}}-{\frac{a}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962989, size = 18, normalized size = 1.06 \begin{align*} -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42594, size = 34, normalized size = 2. \begin{align*} -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.260228, size = 14, normalized size = 0.82 \begin{align*} - \frac{4 a x + 3 b}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1496, size = 18, normalized size = 1.06 \begin{align*} -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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