Optimal. Leaf size=40 \[ -\frac{15}{44} (1-2 x)^{11/2}+\frac{17}{9} (1-2 x)^{9/2}-\frac{11}{4} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0078865, 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} \[ -\frac{15}{44} (1-2 x)^{11/2}+\frac{17}{9} (1-2 x)^{9/2}-\frac{11}{4} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x) (3+5 x) \, dx &=\int \left (\frac{77}{4} (1-2 x)^{5/2}-17 (1-2 x)^{7/2}+\frac{15}{4} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{11}{4} (1-2 x)^{7/2}+\frac{17}{9} (1-2 x)^{9/2}-\frac{15}{44} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0111553, size = 23, normalized size = 0.57 \[ -\frac{1}{99} (1-2 x)^{7/2} \left (135 x^2+239 x+119\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \begin{align*} -{\frac{135\,{x}^{2}+239\,x+119}{99} \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 = 2.66403, size = 38, normalized size = 0.95 \begin{align*} -\frac{15}{44} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{17}{9} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{11}{4} \,{\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 = 1.47228, size = 104, normalized size = 2.6 \begin{align*} \frac{1}{99} \,{\left (1080 \, x^{5} + 292 \, x^{4} - 1106 \, x^{3} - 129 \, x^{2} + 475 \, x - 119\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.57441, size = 85, normalized size = 2.12 \begin{align*} \frac{120 x^{5} \sqrt{1 - 2 x}}{11} + \frac{292 x^{4} \sqrt{1 - 2 x}}{99} - \frac{1106 x^{3} \sqrt{1 - 2 x}}{99} - \frac{43 x^{2} \sqrt{1 - 2 x}}{33} + \frac{475 x \sqrt{1 - 2 x}}{99} - \frac{119 \sqrt{1 - 2 x}}{99} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.73497, size = 66, normalized size = 1.65 \begin{align*} \frac{15}{44} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{17}{9} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{11}{4} \,{\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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