Optimal. Leaf size=5 \[ \frac{x}{c^2} \]
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Rubi [A] time = 0.0027614, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {27, 8} \[ \frac{x}{c^2} \]
Antiderivative was successfully verified.
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Rule 27
Rule 8
Rubi steps
\begin{align*} \int \frac{(d+e x)^4}{\left (c d^2+2 c d e x+c e^2 x^2\right )^2} \, dx &=\int \frac{1}{c^2} \, dx\\ &=\frac{x}{c^2}\\ \end{align*}
Mathematica [A] time = 0.0003174, size = 5, normalized size = 1. \[ \frac{x}{c^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 6, normalized size = 1.2 \begin{align*}{\frac{x}{{c}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08951, size = 7, normalized size = 1.4 \begin{align*} \frac{x}{c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.04359, size = 9, normalized size = 1.8 \begin{align*} \frac{x}{c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12804, size = 3, normalized size = 0.6 \begin{align*} \frac{x}{c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: NotImplementedError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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