Integrand size = 24, antiderivative size = 92 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=-\frac {65219}{64} (1-2 x)^{7/2}+\frac {100793}{48} (1-2 x)^{9/2}-\frac {121359}{64} (1-2 x)^{11/2}+\frac {98209}{104} (1-2 x)^{13/2}-\frac {17337}{64} (1-2 x)^{15/2}+\frac {675}{16} (1-2 x)^{17/2}-\frac {3375 (1-2 x)^{19/2}}{1216} \]
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Time = 0.01 (sec) , antiderivative size = 92, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {90} \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=-\frac {3375 (1-2 x)^{19/2}}{1216}+\frac {675}{16} (1-2 x)^{17/2}-\frac {17337}{64} (1-2 x)^{15/2}+\frac {98209}{104} (1-2 x)^{13/2}-\frac {121359}{64} (1-2 x)^{11/2}+\frac {100793}{48} (1-2 x)^{9/2}-\frac {65219}{64} (1-2 x)^{7/2} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {456533}{64} (1-2 x)^{5/2}-\frac {302379}{16} (1-2 x)^{7/2}+\frac {1334949}{64} (1-2 x)^{9/2}-\frac {98209}{8} (1-2 x)^{11/2}+\frac {260055}{64} (1-2 x)^{13/2}-\frac {11475}{16} (1-2 x)^{15/2}+\frac {3375}{64} (1-2 x)^{17/2}\right ) \, dx \\ & = -\frac {65219}{64} (1-2 x)^{7/2}+\frac {100793}{48} (1-2 x)^{9/2}-\frac {121359}{64} (1-2 x)^{11/2}+\frac {98209}{104} (1-2 x)^{13/2}-\frac {17337}{64} (1-2 x)^{15/2}+\frac {675}{16} (1-2 x)^{17/2}-\frac {3375 (1-2 x)^{19/2}}{1216} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.47 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=-\frac {1}{741} (1-2 x)^{7/2} \left (76018+372070 x+914049 x^2+1346367 x^3+1204398 x^4+605475 x^5+131625 x^6\right ) \]
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Time = 1.00 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.43
method | result | size |
gosper | \(-\frac {\left (1-2 x \right )^{\frac {7}{2}} \left (131625 x^{6}+605475 x^{5}+1204398 x^{4}+1346367 x^{3}+914049 x^{2}+372070 x +76018\right )}{741}\) | \(40\) |
pseudoelliptic | \(\frac {27000 \sqrt {1-2 x}\, \left (x -\frac {1}{2}\right )^{3} \left (x^{6}+\frac {23}{5} x^{5}+\frac {10294}{1125} x^{4}+\frac {448789}{43875} x^{3}+\frac {101561}{14625} x^{2}+\frac {74414}{26325} x +\frac {76018}{131625}\right )}{19}\) | \(43\) |
trager | \(\left (\frac {27000}{19} x^{9}+\frac {83700}{19} x^{8}+\frac {81006}{19} x^{7}-\frac {60205}{247} x^{6}-\frac {741033}{247} x^{5}-\frac {1118224}{741} x^{4}+\frac {281231}{741} x^{3}+\frac {135385}{247} x^{2}+\frac {84038}{741} x -\frac {76018}{741}\right ) \sqrt {1-2 x}\) | \(54\) |
risch | \(-\frac {\left (1053000 x^{9}+3264300 x^{8}+3159234 x^{7}-180615 x^{6}-2223099 x^{5}-1118224 x^{4}+281231 x^{3}+406155 x^{2}+84038 x -76018\right ) \left (-1+2 x \right )}{741 \sqrt {1-2 x}}\) | \(60\) |
derivativedivides | \(-\frac {65219 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {100793 \left (1-2 x \right )^{\frac {9}{2}}}{48}-\frac {121359 \left (1-2 x \right )^{\frac {11}{2}}}{64}+\frac {98209 \left (1-2 x \right )^{\frac {13}{2}}}{104}-\frac {17337 \left (1-2 x \right )^{\frac {15}{2}}}{64}+\frac {675 \left (1-2 x \right )^{\frac {17}{2}}}{16}-\frac {3375 \left (1-2 x \right )^{\frac {19}{2}}}{1216}\) | \(65\) |
default | \(-\frac {65219 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {100793 \left (1-2 x \right )^{\frac {9}{2}}}{48}-\frac {121359 \left (1-2 x \right )^{\frac {11}{2}}}{64}+\frac {98209 \left (1-2 x \right )^{\frac {13}{2}}}{104}-\frac {17337 \left (1-2 x \right )^{\frac {15}{2}}}{64}+\frac {675 \left (1-2 x \right )^{\frac {17}{2}}}{16}-\frac {3375 \left (1-2 x \right )^{\frac {19}{2}}}{1216}\) | \(65\) |
meijerg | \(\frac {\frac {216 \sqrt {\pi }}{7}-\frac {108 \sqrt {\pi }\, \left (-16 x^{3}+24 x^{2}-12 x +2\right ) \sqrt {1-2 x}}{7}}{\sqrt {\pi }}-\frac {7695 \left (-\frac {32 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (-448 x^{4}+608 x^{3}-240 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{945}\right )}{8 \sqrt {\pi }}+\frac {\frac {164 \sqrt {\pi }}{7}-\frac {41 \sqrt {\pi }\, \left (-4032 x^{5}+5152 x^{4}-1808 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{28}}{\sqrt {\pi }}-\frac {256785 \left (-\frac {256 \sqrt {\pi }}{45045}+\frac {2 \sqrt {\pi }\, \left (-118272 x^{6}+145152 x^{5}-47488 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{45045}\right )}{128 \sqrt {\pi }}+\frac {\frac {328 \sqrt {\pi }}{91}-\frac {41 \sqrt {\pi }\, \left (-768768 x^{7}+916608 x^{6}-286272 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{2912}}{\sqrt {\pi }}-\frac {192375 \left (-\frac {4096 \sqrt {\pi }}{2297295}+\frac {4 \sqrt {\pi }\, \left (-9225216 x^{8}+10762752 x^{7}-3252480 x^{6}+8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{2297295}\right )}{512 \sqrt {\pi }}+\frac {\frac {18000 \sqrt {\pi }}{323323}-\frac {1125 \sqrt {\pi }\, \left (-52276224 x^{9}+59963904 x^{8}-17681664 x^{7}+29568 x^{6}+16128 x^{5}+8960 x^{4}+5120 x^{3}+3072 x^{2}+2048 x +2048\right ) \sqrt {1-2 x}}{41385344}}{\sqrt {\pi }}\) | \(373\) |
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Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.59 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=\frac {1}{741} \, {\left (1053000 \, x^{9} + 3264300 \, x^{8} + 3159234 \, x^{7} - 180615 \, x^{6} - 2223099 \, x^{5} - 1118224 \, x^{4} + 281231 \, x^{3} + 406155 \, x^{2} + 84038 \, x - 76018\right )} \sqrt {-2 \, x + 1} \]
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Time = 1.02 (sec) , antiderivative size = 82, normalized size of antiderivative = 0.89 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=- \frac {3375 \left (1 - 2 x\right )^{\frac {19}{2}}}{1216} + \frac {675 \left (1 - 2 x\right )^{\frac {17}{2}}}{16} - \frac {17337 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {98209 \left (1 - 2 x\right )^{\frac {13}{2}}}{104} - \frac {121359 \left (1 - 2 x\right )^{\frac {11}{2}}}{64} + \frac {100793 \left (1 - 2 x\right )^{\frac {9}{2}}}{48} - \frac {65219 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.70 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=-\frac {3375}{1216} \, {\left (-2 \, x + 1\right )}^{\frac {19}{2}} + \frac {675}{16} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {17337}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {98209}{104} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {121359}{64} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {100793}{48} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {65219}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
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Time = 0.29 (sec) , antiderivative size = 113, normalized size of antiderivative = 1.23 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=\frac {3375}{1216} \, {\left (2 \, x - 1\right )}^{9} \sqrt {-2 \, x + 1} + \frac {675}{16} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {17337}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {98209}{104} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {121359}{64} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {100793}{48} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {65219}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
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Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.70 \[ \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx=\frac {100793\,{\left (1-2\,x\right )}^{9/2}}{48}-\frac {65219\,{\left (1-2\,x\right )}^{7/2}}{64}-\frac {121359\,{\left (1-2\,x\right )}^{11/2}}{64}+\frac {98209\,{\left (1-2\,x\right )}^{13/2}}{104}-\frac {17337\,{\left (1-2\,x\right )}^{15/2}}{64}+\frac {675\,{\left (1-2\,x\right )}^{17/2}}{16}-\frac {3375\,{\left (1-2\,x\right )}^{19/2}}{1216} \]
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