Optimal. Leaf size=79 \[ -\frac{9}{224} (2 x+3)^{7/2}+\frac{33}{32} (2 x+3)^{5/2}-\frac{359}{48} (2 x+3)^{3/2}+\frac{651}{16} \sqrt{2 x+3}+\frac{1065}{32 \sqrt{2 x+3}}-\frac{325}{96 (2 x+3)^{3/2}} \]
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Rubi [A] time = 0.026224, 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} \[ -\frac{9}{224} (2 x+3)^{7/2}+\frac{33}{32} (2 x+3)^{5/2}-\frac{359}{48} (2 x+3)^{3/2}+\frac{651}{16} \sqrt{2 x+3}+\frac{1065}{32 \sqrt{2 x+3}}-\frac{325}{96 (2 x+3)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin{align*} \int \frac{(5-x) \left (2+5 x+3 x^2\right )^2}{(3+2 x)^{5/2}} \, dx &=\int \left (\frac{325}{32 (3+2 x)^{5/2}}-\frac{1065}{32 (3+2 x)^{3/2}}+\frac{651}{16 \sqrt{3+2 x}}-\frac{359}{16} \sqrt{3+2 x}+\frac{165}{32} (3+2 x)^{3/2}-\frac{9}{32} (3+2 x)^{5/2}\right ) \, dx\\ &=-\frac{325}{96 (3+2 x)^{3/2}}+\frac{1065}{32 \sqrt{3+2 x}}+\frac{651}{16} \sqrt{3+2 x}-\frac{359}{48} (3+2 x)^{3/2}+\frac{33}{32} (3+2 x)^{5/2}-\frac{9}{224} (3+2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0162293, size = 38, normalized size = 0.48 \[ -\frac{27 x^5-144 x^4-215 x^3-1530 x^2-7164 x-7024}{21 (2 x+3)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{27\,{x}^{5}-144\,{x}^{4}-215\,{x}^{3}-1530\,{x}^{2}-7164\,x-7024}{21} \left ( 3+2\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99555, size = 69, normalized size = 0.87 \begin{align*} -\frac{9}{224} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{33}{32} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{359}{48} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{651}{16} \, \sqrt{2 \, x + 3} + \frac{5 \,{\left (639 \, x + 926\right )}}{48 \,{\left (2 \, x + 3\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83846, size = 130, normalized size = 1.65 \begin{align*} -\frac{{\left (27 \, x^{5} - 144 \, x^{4} - 215 \, x^{3} - 1530 \, x^{2} - 7164 \, x - 7024\right )} \sqrt{2 \, x + 3}}{21 \,{\left (4 \, x^{2} + 12 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 33.5901, size = 70, normalized size = 0.89 \begin{align*} - \frac{9 \left (2 x + 3\right )^{\frac{7}{2}}}{224} + \frac{33 \left (2 x + 3\right )^{\frac{5}{2}}}{32} - \frac{359 \left (2 x + 3\right )^{\frac{3}{2}}}{48} + \frac{651 \sqrt{2 x + 3}}{16} + \frac{1065}{32 \sqrt{2 x + 3}} - \frac{325}{96 \left (2 x + 3\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08219, size = 69, normalized size = 0.87 \begin{align*} -\frac{9}{224} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{33}{32} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{359}{48} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{651}{16} \, \sqrt{2 \, x + 3} + \frac{5 \,{\left (639 \, x + 926\right )}}{48 \,{\left (2 \, x + 3\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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