Optimal. Leaf size=66 \[ -\frac {847}{16} (1-2 x)^{7/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {15}{16} (1-2 x)^{15/2} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {90}
\begin {gather*} -\frac {15}{16} (1-2 x)^{15/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {847}{16} (1-2 x)^{7/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (\frac {5929}{16} (1-2 x)^{5/2}-\frac {1309}{2} (1-2 x)^{7/2}+\frac {3467}{8} (1-2 x)^{9/2}-\frac {255}{2} (1-2 x)^{11/2}+\frac {225}{16} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {847}{16} (1-2 x)^{7/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {15}{16} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 33, normalized size = 0.50 \begin {gather*} -\frac {(1-2 x)^{7/2} \left (13826+50450 x+80307 x^2+62370 x^3+19305 x^4\right )}{1287} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 47, normalized size = 0.71
method | result | size |
gosper | \(-\frac {\left (19305 x^{4}+62370 x^{3}+80307 x^{2}+50450 x +13826\right ) \left (1-2 x \right )^{\frac {7}{2}}}{1287}\) | \(30\) |
trager | \(\left (120 x^{7}+\frac {2700}{13} x^{6}+\frac {1094}{143} x^{5}-\frac {205169}{1287} x^{4}-\frac {75320}{1287} x^{3}+\frac {18827}{429} x^{2}+\frac {32506}{1287} x -\frac {13826}{1287}\right ) \sqrt {1-2 x}\) | \(44\) |
derivativedivides | \(-\frac {847 \left (1-2 x \right )^{\frac {7}{2}}}{16}+\frac {1309 \left (1-2 x \right )^{\frac {9}{2}}}{18}-\frac {3467 \left (1-2 x \right )^{\frac {11}{2}}}{88}+\frac {255 \left (1-2 x \right )^{\frac {13}{2}}}{26}-\frac {15 \left (1-2 x \right )^{\frac {15}{2}}}{16}\) | \(47\) |
default | \(-\frac {847 \left (1-2 x \right )^{\frac {7}{2}}}{16}+\frac {1309 \left (1-2 x \right )^{\frac {9}{2}}}{18}-\frac {3467 \left (1-2 x \right )^{\frac {11}{2}}}{88}+\frac {255 \left (1-2 x \right )^{\frac {13}{2}}}{26}-\frac {15 \left (1-2 x \right )^{\frac {15}{2}}}{16}\) | \(47\) |
risch | \(-\frac {\left (154440 x^{7}+267300 x^{6}+9846 x^{5}-205169 x^{4}-75320 x^{3}+56481 x^{2}+32506 x -13826\right ) \left (-1+2 x \right )}{1287 \sqrt {1-2 x}}\) | \(50\) |
meijerg | \(\frac {\frac {36 \sqrt {\pi }}{7}-\frac {18 \sqrt {\pi }\, \left (-16 x^{3}+24 x^{2}-12 x +2\right ) \sqrt {1-2 x}}{7}}{\sqrt {\pi }}-\frac {855 \left (-\frac {32 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (-448 x^{4}+608 x^{3}-240 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{945}\right )}{8 \sqrt {\pi }}+\frac {\frac {1082 \sqrt {\pi }}{693}-\frac {541 \sqrt {\pi }\, \left (-4032 x^{5}+5152 x^{4}-1808 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{5544}}{\sqrt {\pi }}-\frac {4275 \left (-\frac {256 \sqrt {\pi }}{45045}+\frac {2 \sqrt {\pi }\, \left (-118272 x^{6}+145152 x^{5}-47488 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{45045}\right )}{64 \sqrt {\pi }}+\frac {\frac {40 \sqrt {\pi }}{1001}-\frac {5 \sqrt {\pi }\, \left (-768768 x^{7}+916608 x^{6}-286272 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{32032}}{\sqrt {\pi }}\) | \(242\) |
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 {15}{16} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {255}{26} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {3467}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1309}{18} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {847}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.81, size = 44, normalized size = 0.67 \begin {gather*} \frac {1}{1287} \, {\left (154440 \, x^{7} + 267300 \, x^{6} + 9846 \, x^{5} - 205169 \, x^{4} - 75320 \, x^{3} + 56481 \, x^{2} + 32506 \, x - 13826\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 9.03, size = 58, normalized size = 0.88 \begin {gather*} - \frac {15 \left (1 - 2 x\right )^{\frac {15}{2}}}{16} + \frac {255 \left (1 - 2 x\right )^{\frac {13}{2}}}{26} - \frac {3467 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} + \frac {1309 \left (1 - 2 x\right )^{\frac {9}{2}}}{18} - \frac {847 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.55, size = 81, normalized size = 1.23 \begin {gather*} \frac {15}{16} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {255}{26} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {3467}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1309}{18} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {847}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 0.70 \begin {gather*} \frac {1309\,{\left (1-2\,x\right )}^{9/2}}{18}-\frac {847\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {3467\,{\left (1-2\,x\right )}^{11/2}}{88}+\frac {255\,{\left (1-2\,x\right )}^{13/2}}{26}-\frac {15\,{\left (1-2\,x\right )}^{15/2}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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