Optimal. Leaf size=66 \[ -\frac {9317}{80} (1-2 x)^{5/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {375}{208} (1-2 x)^{13/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 66, normalized size of antiderivative = 1.00, 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 = {78}
\begin {gather*} -\frac {375}{208} (1-2 x)^{13/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {9317}{80} (1-2 x)^{5/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac {9317}{16} (1-2 x)^{3/2}-\frac {8349}{8} (1-2 x)^{5/2}+\frac {2805}{4} (1-2 x)^{7/2}-\frac {1675}{8} (1-2 x)^{9/2}+\frac {375}{16} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {9317}{80} (1-2 x)^{5/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {375}{208} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {(1-2 x)^{5/2} \left (421301+1295695 x+1899800 x^2+1420125 x^3+433125 x^4\right )}{15015} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 47, normalized size = 0.71
method | result | size |
gosper | \(-\frac {\left (433125 x^{4}+1420125 x^{3}+1899800 x^{2}+1295695 x +421301\right ) \left (1-2 x \right )^{\frac {5}{2}}}{15015}\) | \(30\) |
trager | \(\left (-\frac {1500}{13} x^{6}-\frac {37600}{143} x^{5}-\frac {67195}{429} x^{4}+\frac {199259}{3003} x^{3}+\frac {532592}{5005} x^{2}+\frac {389509}{15015} x -\frac {421301}{15015}\right ) \sqrt {1-2 x}\) | \(39\) |
risch | \(\frac {\left (1732500 x^{6}+3948000 x^{5}+2351825 x^{4}-996295 x^{3}-1597776 x^{2}-389509 x +421301\right ) \left (-1+2 x \right )}{15015 \sqrt {1-2 x}}\) | \(45\) |
derivativedivides | \(-\frac {9317 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {8349 \left (1-2 x \right )^{\frac {7}{2}}}{56}-\frac {935 \left (1-2 x \right )^{\frac {9}{2}}}{12}+\frac {1675 \left (1-2 x \right )^{\frac {11}{2}}}{88}-\frac {375 \left (1-2 x \right )^{\frac {13}{2}}}{208}\) | \(47\) |
default | \(-\frac {9317 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {8349 \left (1-2 x \right )^{\frac {7}{2}}}{56}-\frac {935 \left (1-2 x \right )^{\frac {9}{2}}}{12}+\frac {1675 \left (1-2 x \right )^{\frac {11}{2}}}{88}-\frac {375 \left (1-2 x \right )^{\frac {13}{2}}}{208}\) | \(47\) |
meijerg | \(-\frac {81 \left (-\frac {8 \sqrt {\pi }}{15}+\frac {4 \sqrt {\pi }\, \left (8 x^{2}-8 x +2\right ) \sqrt {1-2 x}}{15}\right )}{4 \sqrt {\pi }}+\frac {\frac {351 \sqrt {\pi }}{35}-\frac {351 \sqrt {\pi }\, \left (160 x^{3}-128 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{280}}{\sqrt {\pi }}-\frac {2565 \left (-\frac {64 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (1120 x^{4}-800 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{945}\right )}{32 \sqrt {\pi }}+\frac {\frac {370 \sqrt {\pi }}{231}-\frac {185 \sqrt {\pi }\, \left (26880 x^{5}-17920 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{14784}}{\sqrt {\pi }}-\frac {1125 \left (-\frac {1024 \sqrt {\pi }}{45045}+\frac {4 \sqrt {\pi }\, \left (147840 x^{6}-94080 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{45045}\right )}{128 \sqrt {\pi }}\) | \(217\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 46, normalized size = 0.70 \begin {gather*} -\frac {375}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {1675}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {935}{12} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {8349}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {9317}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.21, size = 39, normalized size = 0.59 \begin {gather*} -\frac {1}{15015} \, {\left (1732500 \, x^{6} + 3948000 \, x^{5} + 2351825 \, x^{4} - 996295 \, x^{3} - 1597776 \, x^{2} - 389509 \, x + 421301\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 10.53, size = 58, normalized size = 0.88 \begin {gather*} - \frac {375 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} + \frac {1675 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {935 \left (1 - 2 x\right )^{\frac {9}{2}}}{12} + \frac {8349 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {9317 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.98, size = 81, normalized size = 1.23 \begin {gather*} -\frac {375}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {1675}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {935}{12} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {8349}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {9317}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 46, normalized size = 0.70 \begin {gather*} \frac {8349\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {9317\,{\left (1-2\,x\right )}^{5/2}}{80}-\frac {935\,{\left (1-2\,x\right )}^{9/2}}{12}+\frac {1675\,{\left (1-2\,x\right )}^{11/2}}{88}-\frac {375\,{\left (1-2\,x\right )}^{13/2}}{208} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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