Optimal. Leaf size=53 \[ -\frac{1}{40} (2 x+3)^{15/2}+\frac{47}{104} (2 x+3)^{13/2}-\frac{109}{88} (2 x+3)^{11/2}+\frac{65}{72} (2 x+3)^{9/2} \]
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Rubi [A] time = 0.015605, 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} \[ -\frac{1}{40} (2 x+3)^{15/2}+\frac{47}{104} (2 x+3)^{13/2}-\frac{109}{88} (2 x+3)^{11/2}+\frac{65}{72} (2 x+3)^{9/2} \]
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 ) \, dx &=\int \left (\frac{65}{8} (3+2 x)^{7/2}-\frac{109}{8} (3+2 x)^{9/2}+\frac{47}{8} (3+2 x)^{11/2}-\frac{3}{8} (3+2 x)^{13/2}\right ) \, dx\\ &=\frac{65}{72} (3+2 x)^{9/2}-\frac{109}{88} (3+2 x)^{11/2}+\frac{47}{104} (3+2 x)^{13/2}-\frac{1}{40} (3+2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.01342, size = 28, normalized size = 0.53 \[ -\frac{(2 x+3)^{9/2} \left (1287 x^3-5841 x^2-10269 x-3727\right )}{6435} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \begin{align*} -{\frac{1287\,{x}^{3}-5841\,{x}^{2}-10269\,x-3727}{6435} \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 = 0.97649, size = 50, normalized size = 0.94 \begin{align*} -\frac{1}{40} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{47}{104} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{109}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{65}{72} \,{\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 = 2.00177, size = 166, normalized size = 3.13 \begin{align*} -\frac{1}{6435} \,{\left (20592 \, x^{7} + 30096 \, x^{6} - 447048 \, x^{5} - 2029120 \, x^{4} - 3733305 \, x^{3} - 3496257 \, x^{2} - 1636821 \, x - 301887\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 5.02764, size = 116, normalized size = 2.19 \begin{align*} - \frac{16 x^{7} \sqrt{2 x + 3}}{5} - \frac{304 x^{6} \sqrt{2 x + 3}}{65} + \frac{49672 x^{5} \sqrt{2 x + 3}}{715} + \frac{405824 x^{4} \sqrt{2 x + 3}}{1287} + \frac{248887 x^{3} \sqrt{2 x + 3}}{429} + \frac{388473 x^{2} \sqrt{2 x + 3}}{715} + \frac{181869 x \sqrt{2 x + 3}}{715} + \frac{33543 \sqrt{2 x + 3}}{715} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10495, size = 50, normalized size = 0.94 \begin{align*} -\frac{1}{40} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{47}{104} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{109}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{65}{72} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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