Optimal. Leaf size=53 \[ \frac{75}{88} (1-2 x)^{11/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{847}{40} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0110615, 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} \[ \frac{75}{88} (1-2 x)^{11/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{847}{40} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac{847}{8} (1-2 x)^{3/2}-\frac{1133}{8} (1-2 x)^{5/2}+\frac{505}{8} (1-2 x)^{7/2}-\frac{75}{8} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{847}{40} (1-2 x)^{5/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{75}{88} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0125818, size = 28, normalized size = 0.53 \[ -\frac{(1-2 x)^{5/2} \left (23625 x^3+61775 x^2+60715 x+24617\right )}{3465} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \begin{align*} -{\frac{23625\,{x}^{3}+61775\,{x}^{2}+60715\,x+24617}{3465} \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 = 2.40354, size = 50, normalized size = 0.94 \begin{align*} \frac{75}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{505}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1133}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{847}{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 = 1.30079, size = 123, normalized size = 2.32 \begin{align*} -\frac{1}{3465} \,{\left (94500 \, x^{5} + 152600 \, x^{4} + 19385 \, x^{3} - 82617 \, x^{2} - 37753 \, x + 24617\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 7.61136, size = 46, normalized size = 0.87 \begin{align*} \frac{75 \left (1 - 2 x\right )^{\frac{11}{2}}}{88} - \frac{505 \left (1 - 2 x\right )^{\frac{9}{2}}}{72} + \frac{1133 \left (1 - 2 x\right )^{\frac{7}{2}}}{56} - \frac{847 \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 = 2.34316, size = 88, normalized size = 1.66 \begin{align*} -\frac{75}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{505}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1133}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{847}{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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