Optimal. Leaf size=105 \[ \frac {3645 (1-2 x)^{13/2}}{1664}-\frac {59049 (1-2 x)^{11/2}}{1408}+\frac {45549}{128} (1-2 x)^{9/2}-\frac {225855}{128} (1-2 x)^{7/2}+\frac {731619}{128} (1-2 x)^{5/2}-\frac {1692705}{128} (1-2 x)^{3/2}+\frac {3916031}{128} \sqrt {1-2 x}+\frac {1294139}{128 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 105, 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 {3645 (1-2 x)^{13/2}}{1664}-\frac {59049 (1-2 x)^{11/2}}{1408}+\frac {45549}{128} (1-2 x)^{9/2}-\frac {225855}{128} (1-2 x)^{7/2}+\frac {731619}{128} (1-2 x)^{5/2}-\frac {1692705}{128} (1-2 x)^{3/2}+\frac {3916031}{128} \sqrt {1-2 x}+\frac {1294139}{128 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {1294139}{128 (1-2 x)^{3/2}}-\frac {3916031}{128 \sqrt {1-2 x}}+\frac {5078115}{128} \sqrt {1-2 x}-\frac {3658095}{128} (1-2 x)^{3/2}+\frac {1580985}{128} (1-2 x)^{5/2}-\frac {409941}{128} (1-2 x)^{7/2}+\frac {59049}{128} (1-2 x)^{9/2}-\frac {3645}{128} (1-2 x)^{11/2}\right ) \, dx\\ &=\frac {1294139}{128 \sqrt {1-2 x}}+\frac {3916031}{128} \sqrt {1-2 x}-\frac {1692705}{128} (1-2 x)^{3/2}+\frac {731619}{128} (1-2 x)^{5/2}-\frac {225855}{128} (1-2 x)^{7/2}+\frac {45549}{128} (1-2 x)^{9/2}-\frac {59049 (1-2 x)^{11/2}}{1408}+\frac {3645 (1-2 x)^{13/2}}{1664}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 48, normalized size = 0.46 \begin {gather*} \frac {-40095 x^7-243486 x^6-687420 x^5-1230120 x^4-1663632 x^3-2109792 x^2-4512448 x+4539904}{143 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 76, normalized size = 0.72 \begin {gather*} \frac {40095 (1-2 x)^7-767637 (1-2 x)^6+6513507 (1-2 x)^5-32297265 (1-2 x)^4+104621517 (1-2 x)^3-242056815 (1-2 x)^2+559992433 (1-2 x)+185061877}{18304 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.49, size = 51, normalized size = 0.49 \begin {gather*} \frac {{\left (40095 \, x^{7} + 243486 \, x^{6} + 687420 \, x^{5} + 1230120 \, x^{4} + 1663632 \, x^{3} + 2109792 \, x^{2} + 4512448 \, x - 4539904\right )} \sqrt {-2 \, x + 1}}{143 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 108, normalized size = 1.03 \begin {gather*} \frac {3645}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {59049}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {45549}{128} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {225855}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {731619}{128} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {1692705}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {3916031}{128} \, \sqrt {-2 \, x + 1} + \frac {1294139}{128 \, \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 = 45, normalized size = 0.43 \begin {gather*} -\frac {40095 x^{7}+243486 x^{6}+687420 x^{5}+1230120 x^{4}+1663632 x^{3}+2109792 x^{2}+4512448 x -4539904}{143 \sqrt {-2 x +1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 73, normalized size = 0.70 \begin {gather*} \frac {3645}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {59049}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {45549}{128} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {225855}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {731619}{128} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {1692705}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {3916031}{128} \, \sqrt {-2 \, x + 1} + \frac {1294139}{128 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 73, normalized size = 0.70 \begin {gather*} \frac {1294139}{128\,\sqrt {1-2\,x}}+\frac {3916031\,\sqrt {1-2\,x}}{128}-\frac {1692705\,{\left (1-2\,x\right )}^{3/2}}{128}+\frac {731619\,{\left (1-2\,x\right )}^{5/2}}{128}-\frac {225855\,{\left (1-2\,x\right )}^{7/2}}{128}+\frac {45549\,{\left (1-2\,x\right )}^{9/2}}{128}-\frac {59049\,{\left (1-2\,x\right )}^{11/2}}{1408}+\frac {3645\,{\left (1-2\,x\right )}^{13/2}}{1664} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 52.64, size = 94, normalized size = 0.90 \begin {gather*} \frac {3645 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} - \frac {59049 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} + \frac {45549 \left (1 - 2 x\right )^{\frac {9}{2}}}{128} - \frac {225855 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} + \frac {731619 \left (1 - 2 x\right )^{\frac {5}{2}}}{128} - \frac {1692705 \left (1 - 2 x\right )^{\frac {3}{2}}}{128} + \frac {3916031 \sqrt {1 - 2 x}}{128} + \frac {1294139}{128 \sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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