Optimal. Leaf size=11 \[ \frac{\log (B-C x)}{C} \]
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Rubi [A] time = 0.0105686, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065, Rules used = {1586, 31} \[ \frac{\log (B-C x)}{C} \]
Antiderivative was successfully verified.
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Rule 1586
Rule 31
Rubi steps
\begin{align*} \int \frac{B^2+B C x+C^2 x^2}{-B^3+C^3 x^3} \, dx &=\int \frac{1}{-B+C x} \, dx\\ &=\frac{\log (B-C x)}{C}\\ \end{align*}
Mathematica [A] time = 0.0015161, size = 12, normalized size = 1.09 \[ \frac{\log (C x-B)}{C} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 12, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( -Cx+B \right ) }{C}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99526, size = 16, normalized size = 1.45 \begin{align*} \frac{\log \left (C x - B\right )}{C} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.918183, size = 22, normalized size = 2. \begin{align*} \frac{\log \left (C x - B\right )}{C} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.068666, size = 7, normalized size = 0.64 \begin{align*} \frac{\log{\left (- B + C x \right )}}{C} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.50249, size = 18, normalized size = 1.64 \begin{align*} \frac{\log \left ({\left | C x - B \right |}\right )}{C} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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