Optimal. Leaf size=17 \[ \frac{(d+e x)^2}{2 c e} \]
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Rubi [A] time = 0.0034212, antiderivative size = 17, 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, 9} \[ \frac{(d+e x)^2}{2 c e} \]
Antiderivative was successfully verified.
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Rule 27
Rule 9
Rubi steps
\begin{align*} \int \frac{(d+e x)^3}{c d^2+2 c d e x+c e^2 x^2} \, dx &=\int \frac{d+e x}{c} \, dx\\ &=\frac{(d+e x)^2}{2 c e}\\ \end{align*}
Mathematica [A] time = 0.0005302, size = 16, normalized size = 0.94 \[ \frac{d x+\frac{e x^2}{2}}{c} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 15, normalized size = 0.9 \begin{align*}{\frac{1}{c} \left ({\frac{e{x}^{2}}{2}}+dx \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.20135, size = 20, normalized size = 1.18 \begin{align*} \frac{e x^{2} + 2 \, d x}{2 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93851, size = 31, normalized size = 1.82 \begin{align*} \frac{e x^{2} + 2 \, d x}{2 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.16671, size = 12, normalized size = 0.71 \begin{align*} \frac{d x}{c} + \frac{e x^{2}}{2 c} \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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