Optimal. Leaf size=5 \[ \frac{x}{c^5} \]
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Rubi [A] time = 0.0013297, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {21, 8} \[ \frac{x}{c^5} \]
Antiderivative was successfully verified.
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Rule 21
Rule 8
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{(a c+b c x)^5} \, dx &=\frac{\int 1 \, dx}{c^5}\\ &=\frac{x}{c^5}\\ \end{align*}
Mathematica [A] time = 0.0003026, size = 5, normalized size = 1. \[ \frac{x}{c^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 6, normalized size = 1.2 \begin{align*}{\frac{x}{{c}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03508, size = 7, normalized size = 1.4 \begin{align*} \frac{x}{c^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45602, size = 9, normalized size = 1.8 \begin{align*} \frac{x}{c^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.098591, size = 3, normalized size = 0.6 \begin{align*} \frac{x}{c^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.07033, size = 20, normalized size = 4. \begin{align*} \frac{b c x + a c}{b c^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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