Optimal. Leaf size=40 \[ -\frac{5}{12} (1-2 x)^{9/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{77}{20} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0081724, antiderivative size = 40, 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} \[ -\frac{5}{12} (1-2 x)^{9/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{77}{20} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x) \, dx &=\int \left (\frac{77}{4} (1-2 x)^{3/2}-17 (1-2 x)^{5/2}+\frac{15}{4} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac{77}{20} (1-2 x)^{5/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{5}{12} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0104367, size = 23, normalized size = 0.57 \[ -\frac{1}{105} (1-2 x)^{5/2} \left (175 x^2+335 x+193\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{\frac{175\,{x}^{2}+335\,x+193}{105} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04005, size = 38, normalized size = 0.95 \begin{align*} -\frac{5}{12} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{17}{7} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{77}{20} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.34833, size = 90, normalized size = 2.25 \begin{align*} -\frac{1}{105} \,{\left (700 \, x^{4} + 640 \, x^{3} - 393 \, x^{2} - 437 \, x + 193\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 5.73067, size = 34, normalized size = 0.85 \begin{align*} - \frac{5 \left (1 - 2 x\right )^{\frac{9}{2}}}{12} + \frac{17 \left (1 - 2 x\right )^{\frac{7}{2}}}{7} - \frac{77 \left (1 - 2 x\right )^{\frac{5}{2}}}{20} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.72287, size = 66, normalized size = 1.65 \begin{align*} -\frac{5}{12} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{17}{7} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{77}{20} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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