Optimal. Leaf size=105 \[ \frac {6075 (1-2 x)^{13/2}}{1664}-\frac {97605 (1-2 x)^{11/2}}{1408}+\frac {74667}{128} (1-2 x)^{9/2}-\frac {367155}{128} (1-2 x)^{7/2}+\frac {1179381}{128} (1-2 x)^{5/2}-\frac {8117095}{384} (1-2 x)^{3/2}+\frac {6206585}{128} \sqrt {1-2 x}+\frac {2033647}{128 \sqrt {1-2 x}} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \[ \frac {6075 (1-2 x)^{13/2}}{1664}-\frac {97605 (1-2 x)^{11/2}}{1408}+\frac {74667}{128} (1-2 x)^{9/2}-\frac {367155}{128} (1-2 x)^{7/2}+\frac {1179381}{128} (1-2 x)^{5/2}-\frac {8117095}{384} (1-2 x)^{3/2}+\frac {6206585}{128} \sqrt {1-2 x}+\frac {2033647}{128 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {2033647}{128 (1-2 x)^{3/2}}-\frac {6206585}{128 \sqrt {1-2 x}}+\frac {8117095}{128} \sqrt {1-2 x}-\frac {5896905}{128} (1-2 x)^{3/2}+\frac {2570085}{128} (1-2 x)^{5/2}-\frac {672003}{128} (1-2 x)^{7/2}+\frac {97605}{128} (1-2 x)^{9/2}-\frac {6075}{128} (1-2 x)^{11/2}\right ) \, dx\\ &=\frac {2033647}{128 \sqrt {1-2 x}}+\frac {6206585}{128} \sqrt {1-2 x}-\frac {8117095}{384} (1-2 x)^{3/2}+\frac {1179381}{128} (1-2 x)^{5/2}-\frac {367155}{128} (1-2 x)^{7/2}+\frac {74667}{128} (1-2 x)^{9/2}-\frac {97605 (1-2 x)^{11/2}}{1408}+\frac {6075 (1-2 x)^{13/2}}{1664}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 0.46 \[ \frac {-200475 x^7-1201635 x^6-3350637 x^5-5928885 x^4-7945164 x^3-10015804 x^2-21370088 x+21493640}{429 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 51, normalized size = 0.49 \[ \frac {{\left (200475 \, x^{7} + 1201635 \, x^{6} + 3350637 \, x^{5} + 5928885 \, x^{4} + 7945164 \, x^{3} + 10015804 \, x^{2} + 21370088 \, x - 21493640\right )} \sqrt {-2 \, x + 1}}{429 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 108, normalized size = 1.03 \[ \frac {6075}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {97605}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {74667}{128} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {367155}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {1179381}{128} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {8117095}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {6206585}{128} \, \sqrt {-2 \, x + 1} + \frac {2033647}{128 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.43 \[ -\frac {200475 x^{7}+1201635 x^{6}+3350637 x^{5}+5928885 x^{4}+7945164 x^{3}+10015804 x^{2}+21370088 x -21493640}{429 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 73, normalized size = 0.70 \[ \frac {6075}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {97605}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {74667}{128} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {367155}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {1179381}{128} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {8117095}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {6206585}{128} \, \sqrt {-2 \, x + 1} + \frac {2033647}{128 \, \sqrt {-2 \, x + 1}} \]
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 \[ \frac {2033647}{128\,\sqrt {1-2\,x}}+\frac {6206585\,\sqrt {1-2\,x}}{128}-\frac {8117095\,{\left (1-2\,x\right )}^{3/2}}{384}+\frac {1179381\,{\left (1-2\,x\right )}^{5/2}}{128}-\frac {367155\,{\left (1-2\,x\right )}^{7/2}}{128}+\frac {74667\,{\left (1-2\,x\right )}^{9/2}}{128}-\frac {97605\,{\left (1-2\,x\right )}^{11/2}}{1408}+\frac {6075\,{\left (1-2\,x\right )}^{13/2}}{1664} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 52.43, size = 94, normalized size = 0.90 \[ \frac {6075 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} - \frac {97605 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} + \frac {74667 \left (1 - 2 x\right )^{\frac {9}{2}}}{128} - \frac {367155 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} + \frac {1179381 \left (1 - 2 x\right )^{\frac {5}{2}}}{128} - \frac {8117095 \left (1 - 2 x\right )^{\frac {3}{2}}}{384} + \frac {6206585 \sqrt {1 - 2 x}}{128} + \frac {2033647}{128 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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