Optimal. Leaf size=79 \[ -\frac {9}{608} (2 x+3)^{19/2}+\frac {165}{544} (2 x+3)^{17/2}-\frac {359}{240} (2 x+3)^{15/2}+\frac {651}{208} (2 x+3)^{13/2}-\frac {1065}{352} (2 x+3)^{11/2}+\frac {325}{288} (2 x+3)^{9/2} \]
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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} \begin {gather*} -\frac {9}{608} (2 x+3)^{19/2}+\frac {165}{544} (2 x+3)^{17/2}-\frac {359}{240} (2 x+3)^{15/2}+\frac {651}{208} (2 x+3)^{13/2}-\frac {1065}{352} (2 x+3)^{11/2}+\frac {325}{288} (2 x+3)^{9/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (5-x) (3+2 x)^{7/2} \left (2+5 x+3 x^2\right )^2 \, dx &=\int \left (\frac {325}{32} (3+2 x)^{7/2}-\frac {1065}{32} (3+2 x)^{9/2}+\frac {651}{16} (3+2 x)^{11/2}-\frac {359}{16} (3+2 x)^{13/2}+\frac {165}{32} (3+2 x)^{15/2}-\frac {9}{32} (3+2 x)^{17/2}\right ) \, dx\\ &=\frac {325}{288} (3+2 x)^{9/2}-\frac {1065}{352} (3+2 x)^{11/2}+\frac {651}{208} (3+2 x)^{13/2}-\frac {359}{240} (3+2 x)^{15/2}+\frac {165}{544} (3+2 x)^{17/2}-\frac {9}{608} (3+2 x)^{19/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \begin {gather*} -\frac {(2 x+3)^{9/2} \left (984555 x^5-2702700 x^4-13495911 x^3-17037702 x^2-8846388 x-1670104\right )}{2078505} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 71, normalized size = 0.90 \begin {gather*} \frac {-984555 (2 x+3)^{19/2}+20173725 (2 x+3)^{17/2}-99491106 (2 x+3)^{15/2}+208170270 (2 x+3)^{13/2}-201237075 (2 x+3)^{11/2}+75057125 (2 x+3)^{9/2}}{66512160} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 54, normalized size = 0.68 \begin {gather*} -\frac {1}{2078505} \, {\left (15752880 \, x^{9} + 51274080 \, x^{8} - 262729896 \, x^{7} - 1939330008 \, x^{6} - 5196312621 \, x^{5} - 7690154020 \, x^{4} - 6844462215 \, x^{3} - 3651616134 \, x^{2} - 1077299892 \, x - 135278424\right )} \sqrt {2 \, x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 55, normalized size = 0.70 \begin {gather*} -\frac {9}{608} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} + \frac {165}{544} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} - \frac {359}{240} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {651}{208} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {1065}{352} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {325}{288} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} \end {gather*}
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 \begin {gather*} -\frac {\left (984555 x^{5}-2702700 x^{4}-13495911 x^{3}-17037702 x^{2}-8846388 x -1670104\right ) \left (2 x +3\right )^{\frac {9}{2}}}{2078505} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 55, normalized size = 0.70 \begin {gather*} -\frac {9}{608} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} + \frac {165}{544} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} - \frac {359}{240} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {651}{208} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {1065}{352} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {325}{288} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.39, size = 55, normalized size = 0.70 \begin {gather*} \frac {325\,{\left (2\,x+3\right )}^{9/2}}{288}-\frac {1065\,{\left (2\,x+3\right )}^{11/2}}{352}+\frac {651\,{\left (2\,x+3\right )}^{13/2}}{208}-\frac {359\,{\left (2\,x+3\right )}^{15/2}}{240}+\frac {165\,{\left (2\,x+3\right )}^{17/2}}{544}-\frac {9\,{\left (2\,x+3\right )}^{19/2}}{608} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.88, size = 146, normalized size = 1.85 \begin {gather*} - \frac {144 x^{9} \sqrt {2 x + 3}}{19} - \frac {7968 x^{8} \sqrt {2 x + 3}}{323} + \frac {612424 x^{7} \sqrt {2 x + 3}}{4845} + \frac {19589192 x^{6} \sqrt {2 x + 3}}{20995} + \frac {577368069 x^{5} \sqrt {2 x + 3}}{230945} + \frac {1538030804 x^{4} \sqrt {2 x + 3}}{415701} + \frac {456297481 x^{3} \sqrt {2 x + 3}}{138567} + \frac {405735126 x^{2} \sqrt {2 x + 3}}{230945} + \frac {119699988 x \sqrt {2 x + 3}}{230945} + \frac {15030936 \sqrt {2 x + 3}}{230945} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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