Optimal. Leaf size=17 \[ -\frac{(a+b x)^2}{2 a x^2} \]
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Rubi [A] time = 0.0017435, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {37} \[ -\frac{(a+b x)^2}{2 a x^2} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{a+b x}{x^3} \, dx &=-\frac{(a+b x)^2}{2 a x^2}\\ \end{align*}
Mathematica [A] time = 0.0015521, size = 15, normalized size = 0.88 \[ -\frac{a}{2 x^2}-\frac{b}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{2\,{x}^{2}}}-{\frac{b}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0543, size = 15, normalized size = 0.88 \begin{align*} -\frac{2 \, b x + a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55443, size = 30, normalized size = 1.76 \begin{align*} -\frac{2 \, b x + a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.383781, size = 12, normalized size = 0.71 \begin{align*} - \frac{a + 2 b x}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1712, size = 15, normalized size = 0.88 \begin{align*} -\frac{2 \, b x + a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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