Optimal. Leaf size=105 \[ -\frac {27 (2 x+3)^{17/2}}{2176}+\frac {189}{640} (2 x+3)^{15/2}-\frac {3519 (2 x+3)^{13/2}}{1664}+\frac {10475 (2 x+3)^{11/2}}{1408}-\frac {17201 (2 x+3)^{9/2}}{1152}+\frac {16005}{896} (2 x+3)^{7/2}-\frac {1585}{128} (2 x+3)^{5/2}+\frac {1625}{384} (2 x+3)^{3/2} \]
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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)^{17/2}}{2176}+\frac {189}{640} (2 x+3)^{15/2}-\frac {3519 (2 x+3)^{13/2}}{1664}+\frac {10475 (2 x+3)^{11/2}}{1408}-\frac {17201 (2 x+3)^{9/2}}{1152}+\frac {16005}{896} (2 x+3)^{7/2}-\frac {1585}{128} (2 x+3)^{5/2}+\frac {1625}{384} (2 x+3)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (5-x) \sqrt {3+2 x} \left (2+5 x+3 x^2\right )^3 \, dx &=\int \left (\frac {1625}{128} \sqrt {3+2 x}-\frac {7925}{128} (3+2 x)^{3/2}+\frac {16005}{128} (3+2 x)^{5/2}-\frac {17201}{128} (3+2 x)^{7/2}+\frac {10475}{128} (3+2 x)^{9/2}-\frac {3519}{128} (3+2 x)^{11/2}+\frac {567}{128} (3+2 x)^{13/2}-\frac {27}{128} (3+2 x)^{15/2}\right ) \, dx\\ &=\frac {1625}{384} (3+2 x)^{3/2}-\frac {1585}{128} (3+2 x)^{5/2}+\frac {16005}{896} (3+2 x)^{7/2}-\frac {17201 (3+2 x)^{9/2}}{1152}+\frac {10475 (3+2 x)^{11/2}}{1408}-\frac {3519 (3+2 x)^{13/2}}{1664}+\frac {189}{640} (3+2 x)^{15/2}-\frac {27 (3+2 x)^{17/2}}{2176}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 48, normalized size = 0.46 \begin {gather*} -\frac {(2 x+3)^{3/2} \left (1216215 x^7-1702701 x^6-20968794 x^5-47286540 x^4-50880095 x^3-29756385 x^2-9013014 x-1197186\right )}{765765} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.06, size = 93, normalized size = 0.89 \begin {gather*} \frac {-1216215 (2 x+3)^{17/2}+28945917 (2 x+3)^{15/2}-207286695 (2 x+3)^{13/2}+729217125 (2 x+3)^{11/2}-1463547085 (2 x+3)^{9/2}+1750866975 (2 x+3)^{7/2}-1213737525 (2 x+3)^{5/2}+414789375 (2 x+3)^{3/2}}{98017920} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 49, normalized size = 0.47 \begin {gather*} -\frac {1}{765765} \, {\left (2432430 \, x^{8} + 243243 \, x^{7} - 47045691 \, x^{6} - 157479462 \, x^{5} - 243619810 \, x^{4} - 212153055 \, x^{3} - 107295183 \, x^{2} - 29433414 \, x - 3591558\right )} \sqrt {2 \, x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 73, normalized size = 0.70 \begin {gather*} -\frac {27}{2176} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} + \frac {189}{640} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} - \frac {3519}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} + \frac {10475}{1408} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} - \frac {17201}{1152} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} + \frac {16005}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} - \frac {1585}{128} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} + \frac {1625}{384} \, {\left (2 \, x + 3\right )}^{\frac {3}{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 (1216215 x^{7}-1702701 x^{6}-20968794 x^{5}-47286540 x^{4}-50880095 x^{3}-29756385 x^{2}-9013014 x -1197186\right ) \left (2 x +3\right )^{\frac {3}{2}}}{765765} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 73, normalized size = 0.70 \begin {gather*} -\frac {27}{2176} \, {\left (2 \, x + 3\right )}^{\frac {17}{2}} + \frac {189}{640} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} - \frac {3519}{1664} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} + \frac {10475}{1408} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} - \frac {17201}{1152} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} + \frac {16005}{896} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} - \frac {1585}{128} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} + \frac {1625}{384} \, {\left (2 \, x + 3\right )}^{\frac {3}{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 {1625\,{\left (2\,x+3\right )}^{3/2}}{384}-\frac {1585\,{\left (2\,x+3\right )}^{5/2}}{128}+\frac {16005\,{\left (2\,x+3\right )}^{7/2}}{896}-\frac {17201\,{\left (2\,x+3\right )}^{9/2}}{1152}+\frac {10475\,{\left (2\,x+3\right )}^{11/2}}{1408}-\frac {3519\,{\left (2\,x+3\right )}^{13/2}}{1664}+\frac {189\,{\left (2\,x+3\right )}^{15/2}}{640}-\frac {27\,{\left (2\,x+3\right )}^{17/2}}{2176} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.02, size = 94, normalized size = 0.90 \begin {gather*} - \frac {27 \left (2 x + 3\right )^{\frac {17}{2}}}{2176} + \frac {189 \left (2 x + 3\right )^{\frac {15}{2}}}{640} - \frac {3519 \left (2 x + 3\right )^{\frac {13}{2}}}{1664} + \frac {10475 \left (2 x + 3\right )^{\frac {11}{2}}}{1408} - \frac {17201 \left (2 x + 3\right )^{\frac {9}{2}}}{1152} + \frac {16005 \left (2 x + 3\right )^{\frac {7}{2}}}{896} - \frac {1585 \left (2 x + 3\right )^{\frac {5}{2}}}{128} + \frac {1625 \left (2 x + 3\right )^{\frac {3}{2}}}{384} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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