Optimal. Leaf size=16 \[ \frac{2 (c+d x)^{5/2}}{5 d} \]
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Rubi [A] time = 0.0014835, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{2 (c+d x)^{5/2}}{5 d} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (c+d x)^{3/2} \, dx &=\frac{2 (c+d x)^{5/2}}{5 d}\\ \end{align*}
Mathematica [A] time = 0.0046322, size = 16, normalized size = 1. \[ \frac{2 (c+d x)^{5/2}}{5 d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*}{\frac{2}{5\,d} \left ( dx+c \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964246, size = 16, normalized size = 1. \begin{align*} \frac{2 \,{\left (d x + c\right )}^{\frac{5}{2}}}{5 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.81845, size = 63, normalized size = 3.94 \begin{align*} \frac{2 \,{\left (d^{2} x^{2} + 2 \, c d x + c^{2}\right )} \sqrt{d x + c}}{5 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.057442, size = 12, normalized size = 0.75 \begin{align*} \frac{2 \left (c + d x\right )^{\frac{5}{2}}}{5 d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06122, size = 16, normalized size = 1. \begin{align*} \frac{2 \,{\left (d x + c\right )}^{\frac{5}{2}}}{5 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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