Optimal. Leaf size=5 \[ c^2 x \]
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Rubi [A] time = 0.0022651, 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} \[ c^2 x \]
Antiderivative was successfully verified.
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Rule 27
Rule 8
Rubi steps
\begin{align*} \int \frac{\left (c d^2+2 c d e x+c e^2 x^2\right )^2}{(d+e x)^4} \, dx &=\int c^2 \, dx\\ &=c^2 x\\ \end{align*}
Mathematica [A] time = 0.0002489, size = 5, normalized size = 1. \[ c^2 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 6, normalized size = 1.2 \begin{align*}{c}^{2}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14836, size = 7, normalized size = 1.4 \begin{align*} c^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.01003, size = 9, normalized size = 1.8 \begin{align*} c^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095872, size = 3, normalized size = 0.6 \begin{align*} c^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16299, size = 7, normalized size = 1.4 \begin{align*} c^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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