Optimal. Leaf size=14 \[ \frac{(c+d x)^4}{4 d} \]
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Rubi [A] time = 0.0099483, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069, Rules used = {626, 32} \[ \frac{(c+d x)^4}{4 d} \]
Antiderivative was successfully verified.
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Rule 626
Rule 32
Rubi steps
\begin{align*} \int \frac{\left (a c+(b c+a d) x+b d x^2\right )^3}{(a+b x)^3} \, dx &=\int (c+d x)^3 \, dx\\ &=\frac{(c+d x)^4}{4 d}\\ \end{align*}
Mathematica [A] time = 0.0015153, size = 14, normalized size = 1. \[ \frac{(c+d x)^4}{4 d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( dx+c \right ) ^{4}}{4\,d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03494, size = 42, normalized size = 3. \begin{align*} \frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, c^{2} d x^{2} + c^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.4753, size = 66, normalized size = 4.71 \begin{align*} \frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, c^{2} d x^{2} + c^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.145323, size = 32, normalized size = 2.29 \begin{align*} c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.22382, size = 42, normalized size = 3. \begin{align*} \frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, c^{2} d x^{2} + c^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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