Optimal. Leaf size=105 \[ -\frac{9}{640} (2 x+3)^{15/2}+\frac{567 (2 x+3)^{13/2}}{1664}-\frac{3519 (2 x+3)^{11/2}}{1408}+\frac{10475 (2 x+3)^{9/2}}{1152}-\frac{17201}{896} (2 x+3)^{7/2}+\frac{3201}{128} (2 x+3)^{5/2}-\frac{7925}{384} (2 x+3)^{3/2}+\frac{1625}{128} \sqrt{2 x+3} \]
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Rubi [A] time = 0.0298382, antiderivative size = 105, 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} \[ -\frac{9}{640} (2 x+3)^{15/2}+\frac{567 (2 x+3)^{13/2}}{1664}-\frac{3519 (2 x+3)^{11/2}}{1408}+\frac{10475 (2 x+3)^{9/2}}{1152}-\frac{17201}{896} (2 x+3)^{7/2}+\frac{3201}{128} (2 x+3)^{5/2}-\frac{7925}{384} (2 x+3)^{3/2}+\frac{1625}{128} \sqrt{2 x+3} \]
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 )^3}{\sqrt{3+2 x}} \, dx &=\int \left (\frac{1625}{128 \sqrt{3+2 x}}-\frac{7925}{128} \sqrt{3+2 x}+\frac{16005}{128} (3+2 x)^{3/2}-\frac{17201}{128} (3+2 x)^{5/2}+\frac{10475}{128} (3+2 x)^{7/2}-\frac{3519}{128} (3+2 x)^{9/2}+\frac{567}{128} (3+2 x)^{11/2}-\frac{27}{128} (3+2 x)^{13/2}\right ) \, dx\\ &=\frac{1625}{128} \sqrt{3+2 x}-\frac{7925}{384} (3+2 x)^{3/2}+\frac{3201}{128} (3+2 x)^{5/2}-\frac{17201}{896} (3+2 x)^{7/2}+\frac{10475 (3+2 x)^{9/2}}{1152}-\frac{3519 (3+2 x)^{11/2}}{1408}+\frac{567 (3+2 x)^{13/2}}{1664}-\frac{9}{640} (3+2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0209207, size = 48, normalized size = 0.46 \[ -\frac{\sqrt{2 x+3} \left (81081 x^7-130977 x^6-1407294 x^5-3109960 x^4-3285105 x^3-1924641 x^2-535098 x-196506\right )}{45045} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 45, normalized size = 0.4 \begin{align*} -{\frac{81081\,{x}^{7}-130977\,{x}^{6}-1407294\,{x}^{5}-3109960\,{x}^{4}-3285105\,{x}^{3}-1924641\,{x}^{2}-535098\,x-196506}{45045}\sqrt{3+2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04672, size = 99, normalized size = 0.94 \begin{align*} -\frac{9}{640} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{567}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{3519}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{10475}{1152} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{17201}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{3201}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{7925}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{1625}{128} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72664, size = 169, normalized size = 1.61 \begin{align*} -\frac{1}{45045} \,{\left (81081 \, x^{7} - 130977 \, x^{6} - 1407294 \, x^{5} - 3109960 \, x^{4} - 3285105 \, x^{3} - 1924641 \, x^{2} - 535098 \, x - 196506\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 105.45, size = 94, normalized size = 0.9 \begin{align*} - \frac{9 \left (2 x + 3\right )^{\frac{15}{2}}}{640} + \frac{567 \left (2 x + 3\right )^{\frac{13}{2}}}{1664} - \frac{3519 \left (2 x + 3\right )^{\frac{11}{2}}}{1408} + \frac{10475 \left (2 x + 3\right )^{\frac{9}{2}}}{1152} - \frac{17201 \left (2 x + 3\right )^{\frac{7}{2}}}{896} + \frac{3201 \left (2 x + 3\right )^{\frac{5}{2}}}{128} - \frac{7925 \left (2 x + 3\right )^{\frac{3}{2}}}{384} + \frac{1625 \sqrt{2 x + 3}}{128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10296, size = 99, normalized size = 0.94 \begin{align*} -\frac{9}{640} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{567}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{3519}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{10475}{1152} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{17201}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{3201}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{7925}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{1625}{128} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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