Optimal. Leaf size=79 \[ -\frac{9}{352} (2 x+3)^{11/2}+\frac{55}{96} (2 x+3)^{9/2}-\frac{359}{112} (2 x+3)^{7/2}+\frac{651}{80} (2 x+3)^{5/2}-\frac{355}{32} (2 x+3)^{3/2}+\frac{325}{32} \sqrt{2 x+3} \]
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Rubi [A] time = 0.0234889, 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} \[ -\frac{9}{352} (2 x+3)^{11/2}+\frac{55}{96} (2 x+3)^{9/2}-\frac{359}{112} (2 x+3)^{7/2}+\frac{651}{80} (2 x+3)^{5/2}-\frac{355}{32} (2 x+3)^{3/2}+\frac{325}{32} \sqrt{2 x+3} \]
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}{\sqrt{3+2 x}} \, dx &=\int \left (\frac{325}{32 \sqrt{3+2 x}}-\frac{1065}{32} \sqrt{3+2 x}+\frac{651}{16} (3+2 x)^{3/2}-\frac{359}{16} (3+2 x)^{5/2}+\frac{165}{32} (3+2 x)^{7/2}-\frac{9}{32} (3+2 x)^{9/2}\right ) \, dx\\ &=\frac{325}{32} \sqrt{3+2 x}-\frac{355}{32} (3+2 x)^{3/2}+\frac{651}{80} (3+2 x)^{5/2}-\frac{359}{112} (3+2 x)^{7/2}+\frac{55}{96} (3+2 x)^{9/2}-\frac{9}{352} (3+2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.01655, size = 38, normalized size = 0.48 \[ -\frac{\sqrt{2 x+3} \left (945 x^5-3500 x^4-12645 x^3-15354 x^2-6252 x-4344\right )}{1155} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \begin{align*} -{\frac{945\,{x}^{5}-3500\,{x}^{4}-12645\,{x}^{3}-15354\,{x}^{2}-6252\,x-4344}{1155}\sqrt{3+2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958316, size = 74, normalized size = 0.94 \begin{align*} -\frac{9}{352} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{55}{96} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{359}{112} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{651}{80} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{355}{32} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{325}{32} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7826, size = 113, normalized size = 1.43 \begin{align*} -\frac{1}{1155} \,{\left (945 \, x^{5} - 3500 \, x^{4} - 12645 \, x^{3} - 15354 \, x^{2} - 6252 \, x - 4344\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 72.3021, size = 70, normalized size = 0.89 \begin{align*} - \frac{9 \left (2 x + 3\right )^{\frac{11}{2}}}{352} + \frac{55 \left (2 x + 3\right )^{\frac{9}{2}}}{96} - \frac{359 \left (2 x + 3\right )^{\frac{7}{2}}}{112} + \frac{651 \left (2 x + 3\right )^{\frac{5}{2}}}{80} - \frac{355 \left (2 x + 3\right )^{\frac{3}{2}}}{32} + \frac{325 \sqrt{2 x + 3}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08663, size = 74, normalized size = 0.94 \begin{align*} -\frac{9}{352} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{55}{96} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{359}{112} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{651}{80} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{355}{32} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{325}{32} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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