Optimal. Leaf size=53 \[ \frac{125}{104} (1-2 x)^{13/2}-\frac{75}{8} (1-2 x)^{11/2}+\frac{605}{24} (1-2 x)^{9/2}-\frac{1331}{56} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0092651, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {43} \[ \frac{125}{104} (1-2 x)^{13/2}-\frac{75}{8} (1-2 x)^{11/2}+\frac{605}{24} (1-2 x)^{9/2}-\frac{1331}{56} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (3+5 x)^3 \, dx &=\int \left (\frac{1331}{8} (1-2 x)^{5/2}-\frac{1815}{8} (1-2 x)^{7/2}+\frac{825}{8} (1-2 x)^{9/2}-\frac{125}{8} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{1331}{56} (1-2 x)^{7/2}+\frac{605}{24} (1-2 x)^{9/2}-\frac{75}{8} (1-2 x)^{11/2}+\frac{125}{104} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0132644, size = 28, normalized size = 0.53 \[ -\frac{1}{273} (1-2 x)^{7/2} \left (2625 x^3+6300 x^2+5495 x+1838\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 25, normalized size = 0.5 \begin{align*} -{\frac{2625\,{x}^{3}+6300\,{x}^{2}+5495\,x+1838}{273} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12376, size = 50, normalized size = 0.94 \begin{align*} \frac{125}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{75}{8} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{605}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{1331}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36454, size = 131, normalized size = 2.47 \begin{align*} \frac{1}{273} \,{\left (21000 \, x^{6} + 18900 \, x^{5} - 15890 \, x^{4} - 16061 \, x^{3} + 4614 \, x^{2} + 5533 \, x - 1838\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.99777, size = 100, normalized size = 1.89 \begin{align*} \frac{1000 x^{6} \sqrt{1 - 2 x}}{13} + \frac{900 x^{5} \sqrt{1 - 2 x}}{13} - \frac{2270 x^{4} \sqrt{1 - 2 x}}{39} - \frac{16061 x^{3} \sqrt{1 - 2 x}}{273} + \frac{1538 x^{2} \sqrt{1 - 2 x}}{91} + \frac{5533 x \sqrt{1 - 2 x}}{273} - \frac{1838 \sqrt{1 - 2 x}}{273} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.23161, size = 88, normalized size = 1.66 \begin{align*} \frac{125}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{75}{8} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{605}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{1331}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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