Optimal. Leaf size=118 \[ -\frac {729}{256} (1-2 x)^{15/2}+\frac {101331 (1-2 x)^{13/2}}{1664}-\frac {821583 (1-2 x)^{11/2}}{1408}+\frac {422919}{128} (1-2 x)^{9/2}-\frac {787185}{64} (1-2 x)^{7/2}+\frac {4084101}{128} (1-2 x)^{5/2}-\frac {7882483}{128} (1-2 x)^{3/2}+\frac {15647317}{128} \sqrt {1-2 x}+\frac {9058973}{256 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 118, 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 {729}{256} (1-2 x)^{15/2}+\frac {101331 (1-2 x)^{13/2}}{1664}-\frac {821583 (1-2 x)^{11/2}}{1408}+\frac {422919}{128} (1-2 x)^{9/2}-\frac {787185}{64} (1-2 x)^{7/2}+\frac {4084101}{128} (1-2 x)^{5/2}-\frac {7882483}{128} (1-2 x)^{3/2}+\frac {15647317}{128} \sqrt {1-2 x}+\frac {9058973}{256 \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)^7 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {9058973}{256 (1-2 x)^{3/2}}-\frac {15647317}{128 \sqrt {1-2 x}}+\frac {23647449}{128} \sqrt {1-2 x}-\frac {20420505}{128} (1-2 x)^{3/2}+\frac {5510295}{64} (1-2 x)^{5/2}-\frac {3806271}{128} (1-2 x)^{7/2}+\frac {821583}{128} (1-2 x)^{9/2}-\frac {101331}{128} (1-2 x)^{11/2}+\frac {10935}{256} (1-2 x)^{13/2}\right ) \, dx\\ &=\frac {9058973}{256 \sqrt {1-2 x}}+\frac {15647317}{128} \sqrt {1-2 x}-\frac {7882483}{128} (1-2 x)^{3/2}+\frac {4084101}{128} (1-2 x)^{5/2}-\frac {787185}{64} (1-2 x)^{7/2}+\frac {422919}{128} (1-2 x)^{9/2}-\frac {821583 (1-2 x)^{11/2}}{1408}+\frac {101331 (1-2 x)^{13/2}}{1664}-\frac {729}{256} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 53, normalized size = 0.45 \begin {gather*} \frac {-104247 x^8-697653 x^7-2168775 x^6-4220622 x^5-5949090 x^4-6921432 x^3-8106616 x^2-16881328 x+16936240}{143 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 85, normalized size = 0.72 \begin {gather*} \frac {-104247 (1-2 x)^8+2229282 (1-2 x)^7-21361158 (1-2 x)^6+120954834 (1-2 x)^5-450269820 (1-2 x)^4+1168052886 (1-2 x)^3-2254390138 (1-2 x)^2+4475132662 (1-2 x)+1295433139}{36608 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 56, normalized size = 0.47 \begin {gather*} \frac {{\left (104247 \, x^{8} + 697653 \, x^{7} + 2168775 \, x^{6} + 4220622 \, x^{5} + 5949090 \, x^{4} + 6921432 \, x^{3} + 8106616 \, x^{2} + 16881328 \, x - 16936240\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 = 1.24, size = 124, normalized size = 1.05 \begin {gather*} \frac {729}{256} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {101331}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {821583}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {422919}{128} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {787185}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {4084101}{128} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {7882483}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {15647317}{128} \, \sqrt {-2 \, x + 1} + \frac {9058973}{256 \, \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 = 50, normalized size = 0.42 \begin {gather*} -\frac {104247 x^{8}+697653 x^{7}+2168775 x^{6}+4220622 x^{5}+5949090 x^{4}+6921432 x^{3}+8106616 x^{2}+16881328 x -16936240}{143 \sqrt {-2 x +1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 82, normalized size = 0.69 \begin {gather*} -\frac {729}{256} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {101331}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {821583}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {422919}{128} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {787185}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {4084101}{128} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {7882483}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {15647317}{128} \, \sqrt {-2 \, x + 1} + \frac {9058973}{256 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.21, size = 82, normalized size = 0.69 \begin {gather*} \frac {9058973}{256\,\sqrt {1-2\,x}}+\frac {15647317\,\sqrt {1-2\,x}}{128}-\frac {7882483\,{\left (1-2\,x\right )}^{3/2}}{128}+\frac {4084101\,{\left (1-2\,x\right )}^{5/2}}{128}-\frac {787185\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {422919\,{\left (1-2\,x\right )}^{9/2}}{128}-\frac {821583\,{\left (1-2\,x\right )}^{11/2}}{1408}+\frac {101331\,{\left (1-2\,x\right )}^{13/2}}{1664}-\frac {729\,{\left (1-2\,x\right )}^{15/2}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 66.05, size = 105, normalized size = 0.89 \begin {gather*} - \frac {729 \left (1 - 2 x\right )^{\frac {15}{2}}}{256} + \frac {101331 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} - \frac {821583 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} + \frac {422919 \left (1 - 2 x\right )^{\frac {9}{2}}}{128} - \frac {787185 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {4084101 \left (1 - 2 x\right )^{\frac {5}{2}}}{128} - \frac {7882483 \left (1 - 2 x\right )^{\frac {3}{2}}}{128} + \frac {15647317 \sqrt {1 - 2 x}}{128} + \frac {9058973}{256 \sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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