Optimal. Leaf size=105 \[ -\frac {9}{896} (2 x+3)^{21/2}+\frac {567 (2 x+3)^{19/2}}{2432}-\frac {207}{128} (2 x+3)^{17/2}+\frac {2095}{384} (2 x+3)^{15/2}-\frac {17201 (2 x+3)^{13/2}}{1664}+\frac {1455}{128} (2 x+3)^{11/2}-\frac {7925 (2 x+3)^{9/2}}{1152}+\frac {1625}{896} (2 x+3)^{7/2} \]
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Rubi [A] time = 0.04, 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} \[ -\frac {9}{896} (2 x+3)^{21/2}+\frac {567 (2 x+3)^{19/2}}{2432}-\frac {207}{128} (2 x+3)^{17/2}+\frac {2095}{384} (2 x+3)^{15/2}-\frac {17201 (2 x+3)^{13/2}}{1664}+\frac {1455}{128} (2 x+3)^{11/2}-\frac {7925 (2 x+3)^{9/2}}{1152}+\frac {1625}{896} (2 x+3)^{7/2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (5-x) (3+2 x)^{5/2} \left (2+5 x+3 x^2\right )^3 \, dx &=\int \left (\frac {1625}{128} (3+2 x)^{5/2}-\frac {7925}{128} (3+2 x)^{7/2}+\frac {16005}{128} (3+2 x)^{9/2}-\frac {17201}{128} (3+2 x)^{11/2}+\frac {10475}{128} (3+2 x)^{13/2}-\frac {3519}{128} (3+2 x)^{15/2}+\frac {567}{128} (3+2 x)^{17/2}-\frac {27}{128} (3+2 x)^{19/2}\right ) \, dx\\ &=\frac {1625}{896} (3+2 x)^{7/2}-\frac {7925 (3+2 x)^{9/2}}{1152}+\frac {1455}{128} (3+2 x)^{11/2}-\frac {17201 (3+2 x)^{13/2}}{1664}+\frac {2095}{384} (3+2 x)^{15/2}-\frac {207}{128} (3+2 x)^{17/2}+\frac {567 (3+2 x)^{19/2}}{2432}-\frac {9}{896} (3+2 x)^{21/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 48, normalized size = 0.46 \[ -\frac {(2 x+3)^{7/2} \left (20007 x^7-22113 x^6-339066 x^5-791700 x^4-871983 x^3-517293 x^2-160006 x-20346\right )}{15561} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 59, normalized size = 0.56 \[ -\frac {1}{15561} \, {\left (160056 \, x^{10} + 543348 \, x^{9} - 2428218 \, x^{8} - 19193889 \, x^{7} - 54383679 \, x^{6} - 87436314 \, x^{5} - 88365578 \, x^{4} - 57400347 \, x^{3} - 23339691 \, x^{2} - 5418846 \, x - 549342\right )} \sqrt {2 \, x + 3} \]
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 \[ -\frac {9}{896} \, {\left (2 \, x + 3\right )}^{\frac {21}{2}} + \frac {567}{2432} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} - \frac {207}{128} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} + \frac {2095}{384} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} - \frac {17201}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} + \frac {1455}{128} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} - \frac {7925}{1152} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} + \frac {1625}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} \]
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 \[ -\frac {\left (20007 x^{7}-22113 x^{6}-339066 x^{5}-791700 x^{4}-871983 x^{3}-517293 x^{2}-160006 x -20346\right ) \left (2 x +3\right )^{\frac {7}{2}}}{15561} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 73, normalized size = 0.70 \[ -\frac {9}{896} \, {\left (2 \, x + 3\right )}^{\frac {21}{2}} + \frac {567}{2432} \, {\left (2 \, x + 3\right )}^{\frac {19}{2}} - \frac {207}{128} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} + \frac {2095}{384} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} - \frac {17201}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} + \frac {1455}{128} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} - \frac {7925}{1152} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} + \frac {1625}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} \]
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 \[ \frac {1625\,{\left (2\,x+3\right )}^{7/2}}{896}-\frac {7925\,{\left (2\,x+3\right )}^{9/2}}{1152}+\frac {1455\,{\left (2\,x+3\right )}^{11/2}}{128}-\frac {17201\,{\left (2\,x+3\right )}^{13/2}}{1664}+\frac {2095\,{\left (2\,x+3\right )}^{15/2}}{384}-\frac {207\,{\left (2\,x+3\right )}^{17/2}}{128}+\frac {567\,{\left (2\,x+3\right )}^{19/2}}{2432}-\frac {9\,{\left (2\,x+3\right )}^{21/2}}{896} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 42.10, size = 94, normalized size = 0.90 \[ - \frac {9 \left (2 x + 3\right )^{\frac {21}{2}}}{896} + \frac {567 \left (2 x + 3\right )^{\frac {19}{2}}}{2432} - \frac {207 \left (2 x + 3\right )^{\frac {17}{2}}}{128} + \frac {2095 \left (2 x + 3\right )^{\frac {15}{2}}}{384} - \frac {17201 \left (2 x + 3\right )^{\frac {13}{2}}}{1664} + \frac {1455 \left (2 x + 3\right )^{\frac {11}{2}}}{128} - \frac {7925 \left (2 x + 3\right )^{\frac {9}{2}}}{1152} + \frac {1625 \left (2 x + 3\right )^{\frac {7}{2}}}{896} \]
Verification of antiderivative is not currently implemented for this CAS.
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