Optimal. Leaf size=6 \[ -\frac{c}{x} \]
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Rubi [A] time = 0.0014597, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087, Rules used = {21, 30} \[ -\frac{c}{x} \]
Antiderivative was successfully verified.
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Rule 21
Rule 30
Rubi steps
\begin{align*} \int \frac{a c+b c x^2}{x^2 \left (a+b x^2\right )} \, dx &=c \int \frac{1}{x^2} \, dx\\ &=-\frac{c}{x}\\ \end{align*}
Mathematica [A] time = 0.0003065, size = 6, normalized size = 1. \[ -\frac{c}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 7, normalized size = 1.2 \begin{align*} -{\frac{c}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.995483, size = 8, normalized size = 1.33 \begin{align*} -\frac{c}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19108, size = 8, normalized size = 1.33 \begin{align*} -\frac{c}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067935, size = 3, normalized size = 0.5 \begin{align*} - \frac{c}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11491, size = 8, normalized size = 1.33 \begin{align*} -\frac{c}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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