Optimal. Leaf size=53 \[ -\frac{1}{24} (2 x+3)^{9/2}+\frac{47}{56} (2 x+3)^{7/2}-\frac{109}{40} (2 x+3)^{5/2}+\frac{65}{24} (2 x+3)^{3/2} \]
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Rubi [A] time = 0.015023, 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} \[ -\frac{1}{24} (2 x+3)^{9/2}+\frac{47}{56} (2 x+3)^{7/2}-\frac{109}{40} (2 x+3)^{5/2}+\frac{65}{24} (2 x+3)^{3/2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin{align*} \int (5-x) \sqrt{3+2 x} \left (2+5 x+3 x^2\right ) \, dx &=\int \left (\frac{65}{8} \sqrt{3+2 x}-\frac{109}{8} (3+2 x)^{3/2}+\frac{47}{8} (3+2 x)^{5/2}-\frac{3}{8} (3+2 x)^{7/2}\right ) \, dx\\ &=\frac{65}{24} (3+2 x)^{3/2}-\frac{109}{40} (3+2 x)^{5/2}+\frac{47}{56} (3+2 x)^{7/2}-\frac{1}{24} (3+2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0112848, size = 28, normalized size = 0.53 \[ -\frac{1}{105} (2 x+3)^{3/2} \left (35 x^3-195 x^2-249 x-101\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.5 \begin{align*} -{\frac{35\,{x}^{3}-195\,{x}^{2}-249\,x-101}{105} \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 = 0.979925, size = 50, normalized size = 0.94 \begin{align*} -\frac{1}{24} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{47}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{109}{40} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{65}{24} \,{\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 = 1.67587, size = 89, normalized size = 1.68 \begin{align*} -\frac{1}{105} \,{\left (70 \, x^{4} - 285 \, x^{3} - 1083 \, x^{2} - 949 \, x - 303\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.13686, size = 44, normalized size = 0.83 \begin{align*} - \frac{\left (2 x + 3\right )^{\frac{9}{2}}}{24} + \frac{47 \left (2 x + 3\right )^{\frac{7}{2}}}{56} - \frac{109 \left (2 x + 3\right )^{\frac{5}{2}}}{40} + \frac{65 \left (2 x + 3\right )^{\frac{3}{2}}}{24} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08475, size = 50, normalized size = 0.94 \begin{align*} -\frac{1}{24} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{47}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{109}{40} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{65}{24} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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