Optimal. Leaf size=53 \[ -\frac{3}{104} (2 x+3)^{13/2}+\frac{47}{88} (2 x+3)^{11/2}-\frac{109}{72} (2 x+3)^{9/2}+\frac{65}{56} (2 x+3)^{7/2} \]
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Rubi [A] time = 0.0155132, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {771} \[ -\frac{3}{104} (2 x+3)^{13/2}+\frac{47}{88} (2 x+3)^{11/2}-\frac{109}{72} (2 x+3)^{9/2}+\frac{65}{56} (2 x+3)^{7/2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin{align*} \int (5-x) (3+2 x)^{5/2} \left (2+5 x+3 x^2\right ) \, dx &=\int \left (\frac{65}{8} (3+2 x)^{5/2}-\frac{109}{8} (3+2 x)^{7/2}+\frac{47}{8} (3+2 x)^{9/2}-\frac{3}{8} (3+2 x)^{11/2}\right ) \, dx\\ &=\frac{65}{56} (3+2 x)^{7/2}-\frac{109}{72} (3+2 x)^{9/2}+\frac{47}{88} (3+2 x)^{11/2}-\frac{3}{104} (3+2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0131499, size = 28, normalized size = 0.53 \[ -\frac{(2 x+3)^{7/2} \left (2079 x^3-9891 x^2-16429 x-5829\right )}{9009} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \begin{align*} -{\frac{2079\,{x}^{3}-9891\,{x}^{2}-16429\,x-5829}{9009} \left ( 3+2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989257, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{104} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{47}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{109}{72} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{65}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68872, size = 144, normalized size = 2.72 \begin{align*} -\frac{1}{9009} \,{\left (16632 \, x^{6} - 4284 \, x^{5} - 375242 \, x^{4} - 1116057 \, x^{3} - 1364067 \, x^{2} - 758349 \, x - 157383\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.11205, size = 100, normalized size = 1.89 \begin{align*} - \frac{24 x^{6} \sqrt{2 x + 3}}{13} + \frac{68 x^{5} \sqrt{2 x + 3}}{143} + \frac{53606 x^{4} \sqrt{2 x + 3}}{1287} + \frac{372019 x^{3} \sqrt{2 x + 3}}{3003} + \frac{151563 x^{2} \sqrt{2 x + 3}}{1001} + \frac{84261 x \sqrt{2 x + 3}}{1001} + \frac{17487 \sqrt{2 x + 3}}{1001} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10623, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{104} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{47}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{109}{72} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{65}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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