Optimal. Leaf size=15 \[ -\frac{a}{x}-\frac{b}{2 x^2} \]
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Rubi [A] time = 0.0047808, antiderivative size = 15, 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} \[ -\frac{a}{x}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+\frac{b}{x}}{x^2} \, dx &=\int \left (\frac{b}{x^3}+\frac{a}{x^2}\right ) \, dx\\ &=-\frac{b}{2 x^2}-\frac{a}{x}\\ \end{align*}
Mathematica [A] time = 0.0015536, size = 15, normalized size = 1. \[ -\frac{a}{x}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 0.9 \begin{align*} -{\frac{b}{2\,{x}^{2}}}-{\frac{a}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.948578, size = 19, normalized size = 1.27 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{2}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4023, size = 30, normalized size = 2. \begin{align*} -\frac{2 \, a x + b}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.247315, size = 12, normalized size = 0.8 \begin{align*} - \frac{2 a x + b}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16599, size = 18, normalized size = 1.2 \begin{align*} -\frac{a}{x} - \frac{b}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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