Optimal. Leaf size=17 \[ \frac{c^2 (d+e x)^2}{2 e} \]
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Rubi [A] time = 0.0035307, 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} \[ \frac{c^2 (d+e x)^2}{2 e} \]
Antiderivative was successfully verified.
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Rule 27
Rule 9
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)^3} \, dx &=\int c^2 (d+e x) \, dx\\ &=\frac{c^2 (d+e x)^2}{2 e}\\ \end{align*}
Mathematica [A] time = 0.000673, size = 16, normalized size = 0.94 \[ c^2 \left (d x+\frac{e x^2}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 15, normalized size = 0.9 \begin{align*}{c}^{2} \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 = 1.16155, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{2} \, c^{2} e x^{2} + c^{2} d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.05921, size = 34, normalized size = 2. \begin{align*} \frac{1}{2} \, c^{2} e x^{2} + c^{2} d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116893, size = 15, normalized size = 0.88 \begin{align*} c^{2} d x + \frac{c^{2} e x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14977, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{2} \,{\left (c^{2} x^{2} e^{7} + 2 \, c^{2} d x e^{6}\right )} e^{\left (-6\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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