Optimal. Leaf size=40 \[ -\frac{25}{44} (1-2 x)^{11/2}+\frac{55}{18} (1-2 x)^{9/2}-\frac{121}{28} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0076592, antiderivative size = 40, 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} \[ -\frac{25}{44} (1-2 x)^{11/2}+\frac{55}{18} (1-2 x)^{9/2}-\frac{121}{28} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (3+5 x)^2 \, dx &=\int \left (\frac{121}{4} (1-2 x)^{5/2}-\frac{55}{2} (1-2 x)^{7/2}+\frac{25}{4} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{121}{28} (1-2 x)^{7/2}+\frac{55}{18} (1-2 x)^{9/2}-\frac{25}{44} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0109682, size = 23, normalized size = 0.57 \[ -\frac{1}{693} (1-2 x)^{7/2} \left (1575 x^2+2660 x+1271\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{\frac{1575\,{x}^{2}+2660\,x+1271}{693} \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 = 2.20678, size = 38, normalized size = 0.95 \begin{align*} -\frac{25}{44} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{55}{18} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{121}{28} \,{\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 = 1.46786, size = 112, normalized size = 2.8 \begin{align*} \frac{1}{693} \,{\left (12600 \, x^{5} + 2380 \, x^{4} - 12302 \, x^{3} - 867 \, x^{2} + 4966 \, x - 1271\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.50879, size = 85, normalized size = 2.12 \begin{align*} \frac{200 x^{5} \sqrt{1 - 2 x}}{11} + \frac{340 x^{4} \sqrt{1 - 2 x}}{99} - \frac{12302 x^{3} \sqrt{1 - 2 x}}{693} - \frac{289 x^{2} \sqrt{1 - 2 x}}{231} + \frac{4966 x \sqrt{1 - 2 x}}{693} - \frac{1271 \sqrt{1 - 2 x}}{693} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.72447, size = 66, normalized size = 1.65 \begin{align*} \frac{25}{44} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{55}{18} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{121}{28} \,{\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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