Optimal. Leaf size=79 \[ -\frac {3}{160} (2 x+3)^{15/2}+\frac {165}{416} (2 x+3)^{13/2}-\frac {359}{176} (2 x+3)^{11/2}+\frac {217}{48} (2 x+3)^{9/2}-\frac {1065}{224} (2 x+3)^{7/2}+\frac {65}{32} (2 x+3)^{5/2} \]
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Rubi [A] time = 0.02, antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {771} \[ -\frac {3}{160} (2 x+3)^{15/2}+\frac {165}{416} (2 x+3)^{13/2}-\frac {359}{176} (2 x+3)^{11/2}+\frac {217}{48} (2 x+3)^{9/2}-\frac {1065}{224} (2 x+3)^{7/2}+\frac {65}{32} (2 x+3)^{5/2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (5-x) (3+2 x)^{3/2} \left (2+5 x+3 x^2\right )^2 \, dx &=\int \left (\frac {325}{32} (3+2 x)^{3/2}-\frac {1065}{32} (3+2 x)^{5/2}+\frac {651}{16} (3+2 x)^{7/2}-\frac {359}{16} (3+2 x)^{9/2}+\frac {165}{32} (3+2 x)^{11/2}-\frac {9}{32} (3+2 x)^{13/2}\right ) \, dx\\ &=\frac {65}{32} (3+2 x)^{5/2}-\frac {1065}{224} (3+2 x)^{7/2}+\frac {217}{48} (3+2 x)^{9/2}-\frac {359}{176} (3+2 x)^{11/2}+\frac {165}{416} (3+2 x)^{13/2}-\frac {3}{160} (3+2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \[ -\frac {(2 x+3)^{5/2} \left (9009 x^5-27720 x^4-124005 x^3-151270 x^2-76260 x-14304\right )}{15015} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 44, normalized size = 0.56 \[ -\frac {1}{15015} \, {\left (36036 \, x^{7} - 2772 \, x^{6} - 747579 \, x^{5} - 2342620 \, x^{4} - 3236325 \, x^{3} - 2333766 \, x^{2} - 857988 \, x - 128736\right )} \sqrt {2 \, x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 55, normalized size = 0.70 \[ -\frac {3}{160} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {165}{416} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {359}{176} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {217}{48} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {1065}{224} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {65}{32} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 35, normalized size = 0.44 \[ -\frac {\left (9009 x^{5}-27720 x^{4}-124005 x^{3}-151270 x^{2}-76260 x -14304\right ) \left (2 x +3\right )^{\frac {5}{2}}}{15015} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 55, normalized size = 0.70 \[ -\frac {3}{160} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {165}{416} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {359}{176} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {217}{48} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {1065}{224} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {65}{32} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 55, normalized size = 0.70 \[ \frac {65\,{\left (2\,x+3\right )}^{5/2}}{32}-\frac {1065\,{\left (2\,x+3\right )}^{7/2}}{224}+\frac {217\,{\left (2\,x+3\right )}^{9/2}}{48}-\frac {359\,{\left (2\,x+3\right )}^{11/2}}{176}+\frac {165\,{\left (2\,x+3\right )}^{13/2}}{416}-\frac {3\,{\left (2\,x+3\right )}^{15/2}}{160} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.80, size = 70, normalized size = 0.89 \[ - \frac {3 \left (2 x + 3\right )^{\frac {15}{2}}}{160} + \frac {165 \left (2 x + 3\right )^{\frac {13}{2}}}{416} - \frac {359 \left (2 x + 3\right )^{\frac {11}{2}}}{176} + \frac {217 \left (2 x + 3\right )^{\frac {9}{2}}}{48} - \frac {1065 \left (2 x + 3\right )^{\frac {7}{2}}}{224} + \frac {65 \left (2 x + 3\right )^{\frac {5}{2}}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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