Optimal. Leaf size=92 \[ -\frac {26411}{64} (1-2 x)^{7/2}+\frac {60025}{72} (1-2 x)^{9/2}-\frac {519645}{704} (1-2 x)^{11/2}+\frac {37485}{104} (1-2 x)^{13/2}-\frac {6489}{64} (1-2 x)^{15/2}+\frac {1053}{68} (1-2 x)^{17/2}-\frac {1215 (1-2 x)^{19/2}}{1216} \]
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Rubi [A]
time = 0.01, antiderivative size = 92, 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 {1215 (1-2 x)^{19/2}}{1216}+\frac {1053}{68} (1-2 x)^{17/2}-\frac {6489}{64} (1-2 x)^{15/2}+\frac {37485}{104} (1-2 x)^{13/2}-\frac {519645}{704} (1-2 x)^{11/2}+\frac {60025}{72} (1-2 x)^{9/2}-\frac {26411}{64} (1-2 x)^{7/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^5 (3+5 x) \, dx &=\int \left (\frac {184877}{64} (1-2 x)^{5/2}-\frac {60025}{8} (1-2 x)^{7/2}+\frac {519645}{64} (1-2 x)^{9/2}-\frac {37485}{8} (1-2 x)^{11/2}+\frac {97335}{64} (1-2 x)^{13/2}-\frac {1053}{4} (1-2 x)^{15/2}+\frac {1215}{64} (1-2 x)^{17/2}\right ) \, dx\\ &=-\frac {26411}{64} (1-2 x)^{7/2}+\frac {60025}{72} (1-2 x)^{9/2}-\frac {519645}{704} (1-2 x)^{11/2}+\frac {37485}{104} (1-2 x)^{13/2}-\frac {6489}{64} (1-2 x)^{15/2}+\frac {1053}{68} (1-2 x)^{17/2}-\frac {1215 (1-2 x)^{19/2}}{1216}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 43, normalized size = 0.47 \begin {gather*} -\frac {(1-2 x)^{7/2} \left (18122584+86950792 x+208370124 x^2+298438668 x^3+259076961 x^4+126243117 x^5+26582985 x^6\right )}{415701} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 65, normalized size = 0.71
method | result | size |
gosper | \(-\frac {\left (26582985 x^{6}+126243117 x^{5}+259076961 x^{4}+298438668 x^{3}+208370124 x^{2}+86950792 x +18122584\right ) \left (1-2 x \right )^{\frac {7}{2}}}{415701}\) | \(40\) |
trager | \(\left (\frac {9720}{19} x^{9}+\frac {536868}{323} x^{8}+\frac {557262}{323} x^{7}+\frac {95571}{4199} x^{6}-\frac {54009375}{46189} x^{5}-\frac {273280105}{415701} x^{4}+\frac {53353244}{415701} x^{3}+\frac {31954540}{138567} x^{2}+\frac {21784712}{415701} x -\frac {18122584}{415701}\right ) \sqrt {1-2 x}\) | \(54\) |
risch | \(-\frac {\left (212663880 x^{9}+690949116 x^{8}+717196194 x^{7}+9461529 x^{6}-486084375 x^{5}-273280105 x^{4}+53353244 x^{3}+95863620 x^{2}+21784712 x -18122584\right ) \left (-1+2 x \right )}{415701 \sqrt {1-2 x}}\) | \(60\) |
derivativedivides | \(-\frac {26411 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {60025 \left (1-2 x \right )^{\frac {9}{2}}}{72}-\frac {519645 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {37485 \left (1-2 x \right )^{\frac {13}{2}}}{104}-\frac {6489 \left (1-2 x \right )^{\frac {15}{2}}}{64}+\frac {1053 \left (1-2 x \right )^{\frac {17}{2}}}{68}-\frac {1215 \left (1-2 x \right )^{\frac {19}{2}}}{1216}\) | \(65\) |
default | \(-\frac {26411 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {60025 \left (1-2 x \right )^{\frac {9}{2}}}{72}-\frac {519645 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {37485 \left (1-2 x \right )^{\frac {13}{2}}}{104}-\frac {6489 \left (1-2 x \right )^{\frac {15}{2}}}{64}+\frac {1053 \left (1-2 x \right )^{\frac {17}{2}}}{68}-\frac {1215 \left (1-2 x \right )^{\frac {19}{2}}}{1216}\) | \(65\) |
meijerg | \(\frac {\frac {96 \sqrt {\pi }}{7}-\frac {48 \sqrt {\pi }\, \left (-16 x^{3}+24 x^{2}-12 x +2\right ) \sqrt {1-2 x}}{7}}{\sqrt {\pi }}-\frac {825 \left (-\frac {32 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (-448 x^{4}+608 x^{3}-240 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{945}\right )}{2 \sqrt {\pi }}+\frac {\frac {320 \sqrt {\pi }}{33}-\frac {20 \sqrt {\pi }\, \left (-4032 x^{5}+5152 x^{4}-1808 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{33}}{\sqrt {\pi }}-\frac {12825 \left (-\frac {256 \sqrt {\pi }}{45045}+\frac {2 \sqrt {\pi }\, \left (-118272 x^{6}+145152 x^{5}-47488 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{45045}\right )}{16 \sqrt {\pi }}+\frac {\frac {1392 \sqrt {\pi }}{1001}-\frac {87 \sqrt {\pi }\, \left (-768768 x^{7}+916608 x^{6}-286272 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{16016}}{\sqrt {\pi }}-\frac {71685 \left (-\frac {4096 \sqrt {\pi }}{2297295}+\frac {4 \sqrt {\pi }\, \left (-9225216 x^{8}+10762752 x^{7}-3252480 x^{6}+8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{2297295}\right )}{512 \sqrt {\pi }}+\frac {\frac {6480 \sqrt {\pi }}{323323}-\frac {405 \sqrt {\pi }\, \left (-52276224 x^{9}+59963904 x^{8}-17681664 x^{7}+29568 x^{6}+16128 x^{5}+8960 x^{4}+5120 x^{3}+3072 x^{2}+2048 x +2048\right ) \sqrt {1-2 x}}{41385344}}{\sqrt {\pi }}\) | \(373\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 64, normalized size = 0.70 \begin {gather*} -\frac {1215}{1216} \, {\left (-2 \, x + 1\right )}^{\frac {19}{2}} + \frac {1053}{68} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {6489}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {37485}{104} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {519645}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {60025}{72} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {26411}{64} \, {\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 = 0.99, size = 54, normalized size = 0.59 \begin {gather*} \frac {1}{415701} \, {\left (212663880 \, x^{9} + 690949116 \, x^{8} + 717196194 \, x^{7} + 9461529 \, x^{6} - 486084375 \, x^{5} - 273280105 \, x^{4} + 53353244 \, x^{3} + 95863620 \, x^{2} + 21784712 \, x - 18122584\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 15.32, size = 82, normalized size = 0.89 \begin {gather*} - \frac {1215 \left (1 - 2 x\right )^{\frac {19}{2}}}{1216} + \frac {1053 \left (1 - 2 x\right )^{\frac {17}{2}}}{68} - \frac {6489 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {37485 \left (1 - 2 x\right )^{\frac {13}{2}}}{104} - \frac {519645 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {60025 \left (1 - 2 x\right )^{\frac {9}{2}}}{72} - \frac {26411 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 113, normalized size = 1.23 \begin {gather*} \frac {1215}{1216} \, {\left (2 \, x - 1\right )}^{9} \sqrt {-2 \, x + 1} + \frac {1053}{68} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {6489}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {37485}{104} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {519645}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {60025}{72} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {26411}{64} \, {\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 = 64, normalized size = 0.70 \begin {gather*} \frac {60025\,{\left (1-2\,x\right )}^{9/2}}{72}-\frac {26411\,{\left (1-2\,x\right )}^{7/2}}{64}-\frac {519645\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {37485\,{\left (1-2\,x\right )}^{13/2}}{104}-\frac {6489\,{\left (1-2\,x\right )}^{15/2}}{64}+\frac {1053\,{\left (1-2\,x\right )}^{17/2}}{68}-\frac {1215\,{\left (1-2\,x\right )}^{19/2}}{1216} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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