Optimal. Leaf size=105 \[ \frac{3375}{896} (1-2 x)^{21/2}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{456533}{128} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0191203, 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} \[ \frac{3375}{896} (1-2 x)^{21/2}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{456533}{128} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (\frac{3195731}{128} (1-2 x)^{5/2}-\frac{9836211}{128} (1-2 x)^{7/2}+\frac{12973191}{128} (1-2 x)^{9/2}-\frac{9504551}{128} (1-2 x)^{11/2}+\frac{4177401}{128} (1-2 x)^{13/2}-\frac{1101465}{128} (1-2 x)^{15/2}+\frac{161325}{128} (1-2 x)^{17/2}-\frac{10125}{128} (1-2 x)^{19/2}\right ) \, dx\\ &=-\frac{456533}{128} (1-2 x)^{7/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{3375}{896} (1-2 x)^{21/2}\\ \end{align*}
Mathematica [A] time = 0.0229051, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{7/2} \left (212574375 x^7+1127763000 x^6+2642319225 x^5+3583371246 x^4+3089723448 x^3+1740153744 x^2+619493392 x+115708576\right )}{440895} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 45, normalized size = 0.4 \begin{align*} -{\frac{212574375\,{x}^{7}+1127763000\,{x}^{6}+2642319225\,{x}^{5}+3583371246\,{x}^{4}+3089723448\,{x}^{3}+1740153744\,{x}^{2}+619493392\,x+115708576}{440895} \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 = 1.52998, size = 99, normalized size = 0.94 \begin{align*} \frac{3375}{896} \,{\left (-2 \, x + 1\right )}^{\frac{21}{2}} - \frac{161325}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} + \frac{1101465}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{1392467}{640} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{9504551}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{1179381}{128} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{3278737}{384} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{456533}{128} \,{\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 = 1.2912, size = 271, normalized size = 2.58 \begin{align*} \frac{1}{440895} \,{\left (1700595000 \, x^{10} + 6471211500 \, x^{9} + 8880844050 \, x^{8} + 3513142893 \, x^{7} - 3556515018 \, x^{6} - 4297543173 \, x^{5} - 970928350 \, x^{4} + 842946920 \, x^{3} + 588303696 \, x^{2} + 74758064 \, x - 115708576\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 23.6528, size = 94, normalized size = 0.9 \begin{align*} \frac{3375 \left (1 - 2 x\right )^{\frac{21}{2}}}{896} - \frac{161325 \left (1 - 2 x\right )^{\frac{19}{2}}}{2432} + \frac{1101465 \left (1 - 2 x\right )^{\frac{17}{2}}}{2176} - \frac{1392467 \left (1 - 2 x\right )^{\frac{15}{2}}}{640} + \frac{9504551 \left (1 - 2 x\right )^{\frac{13}{2}}}{1664} - \frac{1179381 \left (1 - 2 x\right )^{\frac{11}{2}}}{128} + \frac{3278737 \left (1 - 2 x\right )^{\frac{9}{2}}}{384} - \frac{456533 \left (1 - 2 x\right )^{\frac{7}{2}}}{128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.34785, size = 174, normalized size = 1.66 \begin{align*} \frac{3375}{896} \,{\left (2 \, x - 1\right )}^{10} \sqrt{-2 \, x + 1} + \frac{161325}{2432} \,{\left (2 \, x - 1\right )}^{9} \sqrt{-2 \, x + 1} + \frac{1101465}{2176} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{1392467}{640} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{9504551}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{1179381}{128} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{3278737}{384} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{456533}{128} \,{\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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