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 = 0.02, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {771} \begin {gather*} -\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} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{105} (2 x+3)^{3/2} \left (35 x^3-195 x^2-249 x-101\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 49, normalized size = 0.92 \begin {gather*} \frac {1}{840} \left (-35 (2 x+3)^{9/2}+705 (2 x+3)^{7/2}-2289 (2 x+3)^{5/2}+2275 (2 x+3)^{3/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 29, normalized size = 0.55 \begin {gather*} -\frac {1}{105} \, {\left (70 \, x^{4} - 285 \, x^{3} - 1083 \, x^{2} - 949 \, x - 303\right )} \sqrt {2 \, x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 37, normalized size = 0.70 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.47 \begin {gather*} -\frac {\left (35 x^{3}-195 x^{2}-249 x -101\right ) \left (2 x +3\right )^{\frac {3}{2}}}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 37, normalized size = 0.70 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.70 \begin {gather*} \frac {65\,{\left (2\,x+3\right )}^{3/2}}{24}-\frac {109\,{\left (2\,x+3\right )}^{5/2}}{40}+\frac {47\,{\left (2\,x+3\right )}^{7/2}}{56}-\frac {{\left (2\,x+3\right )}^{9/2}}{24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.70, size = 44, normalized size = 0.83 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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