Optimal. Leaf size=105 \[ -\frac {27 (2 x+3)^{19/2}}{2432}+\frac {567 (2 x+3)^{17/2}}{2176}-\frac {1173}{640} (2 x+3)^{15/2}+\frac {10475 (2 x+3)^{13/2}}{1664}-\frac {17201 (2 x+3)^{11/2}}{1408}+\frac {5335}{384} (2 x+3)^{9/2}-\frac {7925}{896} (2 x+3)^{7/2}+\frac {325}{128} (2 x+3)^{5/2} \]
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Rubi [A] time = 0.03, antiderivative size = 105, 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 {27 (2 x+3)^{19/2}}{2432}+\frac {567 (2 x+3)^{17/2}}{2176}-\frac {1173}{640} (2 x+3)^{15/2}+\frac {10475 (2 x+3)^{13/2}}{1664}-\frac {17201 (2 x+3)^{11/2}}{1408}+\frac {5335}{384} (2 x+3)^{9/2}-\frac {7925}{896} (2 x+3)^{7/2}+\frac {325}{128} (2 x+3)^{5/2} \end {gather*}
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 )^3 \, dx &=\int \left (\frac {1625}{128} (3+2 x)^{3/2}-\frac {7925}{128} (3+2 x)^{5/2}+\frac {16005}{128} (3+2 x)^{7/2}-\frac {17201}{128} (3+2 x)^{9/2}+\frac {10475}{128} (3+2 x)^{11/2}-\frac {3519}{128} (3+2 x)^{13/2}+\frac {567}{128} (3+2 x)^{15/2}-\frac {27}{128} (3+2 x)^{17/2}\right ) \, dx\\ &=\frac {325}{128} (3+2 x)^{5/2}-\frac {7925}{896} (3+2 x)^{7/2}+\frac {5335}{384} (3+2 x)^{9/2}-\frac {17201 (3+2 x)^{11/2}}{1408}+\frac {10475 (3+2 x)^{13/2}}{1664}-\frac {1173}{640} (3+2 x)^{15/2}+\frac {567 (3+2 x)^{17/2}}{2176}-\frac {27 (3+2 x)^{19/2}}{2432}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 48, normalized size = 0.46 \begin {gather*} -\frac {(2 x+3)^{5/2} \left (6891885 x^7-8513505 x^6-117819702 x^5-270695040 x^4-295054725 x^3-173763625 x^2-53367570 x-6778218\right )}{4849845} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.05, size = 93, normalized size = 0.89 \begin {gather*} \frac {-6891885 (2 x+3)^{19/2}+161756595 (2 x+3)^{17/2}-1137773637 (2 x+3)^{15/2}+3907855875 (2 x+3)^{13/2}-7583834895 (2 x+3)^{11/2}+8624641025 (2 x+3)^{9/2}-5490717375 (2 x+3)^{7/2}+1576199625 (2 x+3)^{5/2}}{620780160} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 54, normalized size = 0.51 \begin {gather*} -\frac {1}{4849845} \, {\left (27567540 \, x^{9} + 48648600 \, x^{8} - 511413903 \, x^{7} - 2573238129 \, x^{6} - 5488936698 \, x^{5} - 6671966560 \, x^{4} - 4954126305 \, x^{3} - 2231396337 \, x^{2} - 561646746 \, x - 61003962\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 = 73, normalized size = 0.70 \begin {gather*} -\frac {27}{2432} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} + \frac {567}{2176} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} - \frac {1173}{640} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {10475}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {17201}{1408} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {5335}{384} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {7925}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {325}{128} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} \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 {\left (6891885 x^{7}-8513505 x^{6}-117819702 x^{5}-270695040 x^{4}-295054725 x^{3}-173763625 x^{2}-53367570 x -6778218\right ) \left (2 x +3\right )^{\frac {5}{2}}}{4849845} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 73, normalized size = 0.70 \begin {gather*} -\frac {27}{2432} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} + \frac {567}{2176} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} - \frac {1173}{640} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {10475}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {17201}{1408} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {5335}{384} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {7925}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {325}{128} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 73, normalized size = 0.70 \begin {gather*} \frac {325\,{\left (2\,x+3\right )}^{5/2}}{128}-\frac {7925\,{\left (2\,x+3\right )}^{7/2}}{896}+\frac {5335\,{\left (2\,x+3\right )}^{9/2}}{384}-\frac {17201\,{\left (2\,x+3\right )}^{11/2}}{1408}+\frac {10475\,{\left (2\,x+3\right )}^{13/2}}{1664}-\frac {1173\,{\left (2\,x+3\right )}^{15/2}}{640}+\frac {567\,{\left (2\,x+3\right )}^{17/2}}{2176}-\frac {27\,{\left (2\,x+3\right )}^{19/2}}{2432} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 35.46, size = 94, normalized size = 0.90 \begin {gather*} - \frac {27 \left (2 x + 3\right )^{\frac {19}{2}}}{2432} + \frac {567 \left (2 x + 3\right )^{\frac {17}{2}}}{2176} - \frac {1173 \left (2 x + 3\right )^{\frac {15}{2}}}{640} + \frac {10475 \left (2 x + 3\right )^{\frac {13}{2}}}{1664} - \frac {17201 \left (2 x + 3\right )^{\frac {11}{2}}}{1408} + \frac {5335 \left (2 x + 3\right )^{\frac {9}{2}}}{384} - \frac {7925 \left (2 x + 3\right )^{\frac {7}{2}}}{896} + \frac {325 \left (2 x + 3\right )^{\frac {5}{2}}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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