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 = 0.0238475, antiderivative size = 79, normalized size of antiderivative = 1., 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} \[ -\frac{9}{608} (2 x+3)^{19/2}+\frac{165}{544} (2 x+3)^{17/2}-\frac{359}{240} (2 x+3)^{15/2}+\frac{651}{208} (2 x+3)^{13/2}-\frac{1065}{352} (2 x+3)^{11/2}+\frac{325}{288} (2 x+3)^{9/2} \]
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*}
Mathematica [A] time = 0.0184268, size = 38, normalized size = 0.48 \[ -\frac{(2 x+3)^{9/2} \left (984555 x^5-2702700 x^4-13495911 x^3-17037702 x^2-8846388 x-1670104\right )}{2078505} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \begin{align*} -{\frac{984555\,{x}^{5}-2702700\,{x}^{4}-13495911\,{x}^{3}-17037702\,{x}^{2}-8846388\,x-1670104}{2078505} \left ( 3+2\,x \right ) ^{{\frac{9}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03454, size = 74, normalized size = 0.94 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77293, size = 248, normalized size = 3.14 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 8.23465, size = 146, normalized size = 1.85 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11218, size = 74, normalized size = 0.94 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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