Optimal. Leaf size=38 \[ -\frac{5}{4} (1-2 x)^{3/2}+17 \sqrt{1-2 x}+\frac{77}{4 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0080628, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{5}{4} (1-2 x)^{3/2}+17 \sqrt{1-2 x}+\frac{77}{4 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{77}{4 (1-2 x)^{3/2}}-\frac{17}{\sqrt{1-2 x}}+\frac{15}{4} \sqrt{1-2 x}\right ) \, dx\\ &=\frac{77}{4 \sqrt{1-2 x}}+17 \sqrt{1-2 x}-\frac{5}{4} (1-2 x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0080641, size = 20, normalized size = 0.53 \[ \frac{-5 x^2-29 x+35}{\sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{(5\,{x}^{2}+29\,x-35){\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.5571, size = 38, normalized size = 1. \begin{align*} -\frac{5}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 17 \, \sqrt{-2 \, x + 1} + \frac{77}{4 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64117, size = 62, normalized size = 1.63 \begin{align*} \frac{{\left (5 \, x^{2} + 29 \, x - 35\right )} \sqrt{-2 \, x + 1}}{2 \, x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 7.50867, size = 32, normalized size = 0.84 \begin{align*} - \frac{5 \left (1 - 2 x\right )^{\frac{3}{2}}}{4} + 17 \sqrt{1 - 2 x} + \frac{77}{4 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.51225, size = 38, normalized size = 1. \begin{align*} -\frac{5}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 17 \, \sqrt{-2 \, x + 1} + \frac{77}{4 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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