Optimal. Leaf size=20 \[ \frac{(a e+c d x)^4}{4 c d} \]
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Rubi [A] time = 0.0133856, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.057, Rules used = {626, 32} \[ \frac{(a e+c d x)^4}{4 c d} \]
Antiderivative was successfully verified.
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Rule 626
Rule 32
Rubi steps
\begin{align*} \int \frac{\left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^3}{(d+e x)^3} \, dx &=\int (a e+c d x)^3 \, dx\\ &=\frac{(a e+c d x)^4}{4 c d}\\ \end{align*}
Mathematica [A] time = 0.0025022, size = 20, normalized size = 1. \[ \frac{(a e+c d x)^4}{4 c d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 19, normalized size = 1. \begin{align*}{\frac{ \left ( cdx+ae \right ) ^{4}}{4\,cd}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.08492, size = 61, normalized size = 3.05 \begin{align*} \frac{1}{4} \, c^{3} d^{3} x^{4} + a c^{2} d^{2} e x^{3} + \frac{3}{2} \, a^{2} c d e^{2} x^{2} + a^{3} e^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.52203, size = 93, normalized size = 4.65 \begin{align*} \frac{1}{4} \, c^{3} d^{3} x^{4} + a c^{2} d^{2} e x^{3} + \frac{3}{2} \, a^{2} c d e^{2} x^{2} + a^{3} e^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.137744, size = 49, normalized size = 2.45 \begin{align*} a^{3} e^{3} x + \frac{3 a^{2} c d e^{2} x^{2}}{2} + a c^{2} d^{2} e x^{3} + \frac{c^{3} d^{3} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.23946, size = 69, normalized size = 3.45 \begin{align*} \frac{1}{4} \,{\left (c^{3} d^{3} x^{4} e^{12} + 4 \, a c^{2} d^{2} x^{3} e^{13} + 6 \, a^{2} c d x^{2} e^{14} + 4 \, a^{3} x e^{15}\right )} e^{\left (-12\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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