Optimal. Leaf size=53 \[ \frac{45}{88} (1-2 x)^{11/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{539}{40} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0099535, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {77} \[ \frac{45}{88} (1-2 x)^{11/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{539}{40} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x) \, dx &=\int \left (\frac{539}{8} (1-2 x)^{3/2}-\frac{707}{8} (1-2 x)^{5/2}+\frac{309}{8} (1-2 x)^{7/2}-\frac{45}{8} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{539}{40} (1-2 x)^{5/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{45}{88} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0127899, size = 28, normalized size = 0.53 \[ -\frac{1}{165} (1-2 x)^{5/2} \left (675 x^3+1820 x^2+1840 x+764\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 25, normalized size = 0.5 \begin{align*} -{\frac{675\,{x}^{3}+1820\,{x}^{2}+1840\,x+764}{165} \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 = 1.39208, size = 50, normalized size = 0.94 \begin{align*} \frac{45}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{103}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{101}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{539}{40} \,{\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 = 1.30718, size = 109, normalized size = 2.06 \begin{align*} -\frac{1}{165} \,{\left (2700 \, x^{5} + 4580 \, x^{4} + 755 \, x^{3} - 2484 \, x^{2} - 1216 \, x + 764\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 7.76258, size = 46, normalized size = 0.87 \begin{align*} \frac{45 \left (1 - 2 x\right )^{\frac{11}{2}}}{88} - \frac{103 \left (1 - 2 x\right )^{\frac{9}{2}}}{24} + \frac{101 \left (1 - 2 x\right )^{\frac{7}{2}}}{8} - \frac{539 \left (1 - 2 x\right )^{\frac{5}{2}}}{40} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.11521, size = 88, normalized size = 1.66 \begin{align*} -\frac{45}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{103}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{101}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{539}{40} \,{\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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