Optimal. Leaf size=53 \[ -\frac{3}{56} (2 x+3)^{7/2}+\frac{47}{40} (2 x+3)^{5/2}-\frac{109}{24} (2 x+3)^{3/2}+\frac{65}{8} \sqrt{2 x+3} \]
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Rubi [A] time = 0.0161647, 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} \[ -\frac{3}{56} (2 x+3)^{7/2}+\frac{47}{40} (2 x+3)^{5/2}-\frac{109}{24} (2 x+3)^{3/2}+\frac{65}{8} \sqrt{2 x+3} \]
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 )}{\sqrt{3+2 x}} \, dx &=\int \left (\frac{65}{8 \sqrt{3+2 x}}-\frac{109}{8} \sqrt{3+2 x}+\frac{47}{8} (3+2 x)^{3/2}-\frac{3}{8} (3+2 x)^{5/2}\right ) \, dx\\ &=\frac{65}{8} \sqrt{3+2 x}-\frac{109}{24} (3+2 x)^{3/2}+\frac{47}{40} (3+2 x)^{5/2}-\frac{3}{56} (3+2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0115379, size = 28, normalized size = 0.53 \[ -\frac{1}{105} \sqrt{2 x+3} \left (45 x^3-291 x^2-223 x-381\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.5 \begin{align*} -{\frac{45\,{x}^{3}-291\,{x}^{2}-223\,x-381}{105}\sqrt{3+2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0178, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{47}{40} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{109}{24} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{65}{8} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66431, size = 74, normalized size = 1.4 \begin{align*} -\frac{1}{105} \,{\left (45 \, x^{3} - 291 \, x^{2} - 223 \, x - 381\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 34.2836, size = 46, normalized size = 0.87 \begin{align*} - \frac{3 \left (2 x + 3\right )^{\frac{7}{2}}}{56} + \frac{47 \left (2 x + 3\right )^{\frac{5}{2}}}{40} - \frac{109 \left (2 x + 3\right )^{\frac{3}{2}}}{24} + \frac{65 \sqrt{2 x + 3}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11009, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{47}{40} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{109}{24} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{65}{8} \, \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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