Optimal. Leaf size=105 \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.019335, antiderivative size = 105, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {88} \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (\frac{3195731}{128} (1-2 x)^{3/2}-\frac{9836211}{128} (1-2 x)^{5/2}+\frac{12973191}{128} (1-2 x)^{7/2}-\frac{9504551}{128} (1-2 x)^{9/2}+\frac{4177401}{128} (1-2 x)^{11/2}-\frac{1101465}{128} (1-2 x)^{13/2}+\frac{161325}{128} (1-2 x)^{15/2}-\frac{10125}{128} (1-2 x)^{17/2}\right ) \, dx\\ &=-\frac{3195731}{640} (1-2 x)^{5/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{10125 (1-2 x)^{19/2}}{2432}\\ \end{align*}
Mathematica [A] time = 0.0229892, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{5/2} \left (369208125 x^7+1995171750 x^6+4795033815 x^5+6744559140 x^4+6142984080 x^3+3771434840 x^2+1547888800 x+369438704\right )}{692835} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 45, normalized size = 0.4 \begin{align*} -{\frac{369208125\,{x}^{7}+1995171750\,{x}^{6}+4795033815\,{x}^{5}+6744559140\,{x}^{4}+6142984080\,{x}^{3}+3771434840\,{x}^{2}+1547888800\,x+369438704}{692835} \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 = 2.22928, size = 99, normalized size = 0.94 \begin{align*} \frac{10125}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} - \frac{161325}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} + \frac{73431}{128} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{4177401}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{9504551}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{4324397}{384} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1405173}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3195731}{640} \,{\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 = 1.36473, size = 252, normalized size = 2.4 \begin{align*} -\frac{1}{692835} \,{\left (1476832500 \, x^{9} + 6503854500 \, x^{8} + 11568656385 \, x^{7} + 9793273050 \, x^{6} + 2388733575 \, x^{5} - 2741637820 \, x^{4} - 2751200080 \, x^{3} - 942365544 \, x^{2} + 70133984 \, x + 369438704\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 19.1283, size = 94, normalized size = 0.9 \begin{align*} \frac{10125 \left (1 - 2 x\right )^{\frac{19}{2}}}{2432} - \frac{161325 \left (1 - 2 x\right )^{\frac{17}{2}}}{2176} + \frac{73431 \left (1 - 2 x\right )^{\frac{15}{2}}}{128} - \frac{4177401 \left (1 - 2 x\right )^{\frac{13}{2}}}{1664} + \frac{9504551 \left (1 - 2 x\right )^{\frac{11}{2}}}{1408} - \frac{4324397 \left (1 - 2 x\right )^{\frac{9}{2}}}{384} + \frac{1405173 \left (1 - 2 x\right )^{\frac{7}{2}}}{128} - \frac{3195731 \left (1 - 2 x\right )^{\frac{5}{2}}}{640} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.5453, size = 174, normalized size = 1.66 \begin{align*} -\frac{10125}{2432} \,{\left (2 \, x - 1\right )}^{9} \sqrt{-2 \, x + 1} - \frac{161325}{2176} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} - \frac{73431}{128} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} - \frac{4177401}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{9504551}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{4324397}{384} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1405173}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3195731}{640} \,{\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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