Optimal. Leaf size=53 \[ -\frac {3}{88} (2 x+3)^{11/2}+\frac {47}{72} (2 x+3)^{9/2}-\frac {109}{56} (2 x+3)^{7/2}+\frac {13}{8} (2 x+3)^{5/2} \]
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Rubi [A] time = 0.02, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {771} \begin {gather*} -\frac {3}{88} (2 x+3)^{11/2}+\frac {47}{72} (2 x+3)^{9/2}-\frac {109}{56} (2 x+3)^{7/2}+\frac {13}{8} (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 ) \, dx &=\int \left (\frac {65}{8} (3+2 x)^{3/2}-\frac {109}{8} (3+2 x)^{5/2}+\frac {47}{8} (3+2 x)^{7/2}-\frac {3}{8} (3+2 x)^{9/2}\right ) \, dx\\ &=\frac {13}{8} (3+2 x)^{5/2}-\frac {109}{56} (3+2 x)^{7/2}+\frac {47}{72} (3+2 x)^{9/2}-\frac {3}{88} (3+2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{693} (2 x+3)^{5/2} \left (189 x^3-959 x^2-1455 x-513\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 49, normalized size = 0.92 \begin {gather*} \frac {-189 (2 x+3)^{11/2}+3619 (2 x+3)^{9/2}-10791 (2 x+3)^{7/2}+9009 (2 x+3)^{5/2}}{5544} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 34, normalized size = 0.64 \begin {gather*} -\frac {1}{693} \, {\left (756 \, x^{5} - 1568 \, x^{4} - 15627 \, x^{3} - 28143 \, x^{2} - 19251 \, x - 4617\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 = 37, normalized size = 0.70 \begin {gather*} -\frac {3}{88} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {47}{72} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {109}{56} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {13}{8} \, {\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 = 25, normalized size = 0.47 \begin {gather*} -\frac {\left (189 x^{3}-959 x^{2}-1455 x -513\right ) \left (2 x +3\right )^{\frac {5}{2}}}{693} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 37, normalized size = 0.70 \begin {gather*} -\frac {3}{88} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {47}{72} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} - \frac {109}{56} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {13}{8} \, {\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 = 0.04, size = 37, normalized size = 0.70 \begin {gather*} \frac {13\,{\left (2\,x+3\right )}^{5/2}}{8}-\frac {109\,{\left (2\,x+3\right )}^{7/2}}{56}+\frac {47\,{\left (2\,x+3\right )}^{9/2}}{72}-\frac {3\,{\left (2\,x+3\right )}^{11/2}}{88} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.96, size = 46, normalized size = 0.87 \begin {gather*} - \frac {3 \left (2 x + 3\right )^{\frac {11}{2}}}{88} + \frac {47 \left (2 x + 3\right )^{\frac {9}{2}}}{72} - \frac {109 \left (2 x + 3\right )^{\frac {7}{2}}}{56} + \frac {13 \left (2 x + 3\right )^{\frac {5}{2}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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