Optimal. Leaf size=92 \[ -\frac {1215 (1-2 x)^{19/2}}{1216}+\frac {1053}{68} (1-2 x)^{17/2}-\frac {6489}{64} (1-2 x)^{15/2}+\frac {37485}{104} (1-2 x)^{13/2}-\frac {519645}{704} (1-2 x)^{11/2}+\frac {60025}{72} (1-2 x)^{9/2}-\frac {26411}{64} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.02, 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 = {77} \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 77
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 (26582985 x^6+126243117 x^5+259076961 x^4+298438668 x^3+208370124 x^2+86950792 x+18122584\right )}{415701} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 82, normalized size = 0.89 \begin {gather*} \frac {-26582985 (1-2 x)^{19/2}+411984144 (1-2 x)^{17/2}-2697483789 (1-2 x)^{15/2}+9589262760 (1-2 x)^{13/2}-19637904195 (1-2 x)^{11/2}+22179957800 (1-2 x)^{9/2}-10979079111 (1-2 x)^{7/2}}{26604864} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, 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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giac [A] time = 0.92, 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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maple [A] time = 0.00, size = 40, normalized size = 0.43 \begin {gather*} -\frac {\left (26582985 x^{6}+126243117 x^{5}+259076961 x^{4}+298438668 x^{3}+208370124 x^{2}+86950792 x +18122584\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{415701} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, 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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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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sympy [A] time = 25.70, 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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