Optimal. Leaf size=79 \[ -\frac {9}{224} (2 x+3)^{7/2}+\frac {33}{32} (2 x+3)^{5/2}-\frac {359}{48} (2 x+3)^{3/2}+\frac {651}{16} \sqrt {2 x+3}+\frac {1065}{32 \sqrt {2 x+3}}-\frac {325}{96 (2 x+3)^{3/2}} \]
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Rubi [A] time = 0.03, antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {771} \begin {gather*} -\frac {9}{224} (2 x+3)^{7/2}+\frac {33}{32} (2 x+3)^{5/2}-\frac {359}{48} (2 x+3)^{3/2}+\frac {651}{16} \sqrt {2 x+3}+\frac {1065}{32 \sqrt {2 x+3}}-\frac {325}{96 (2 x+3)^{3/2}} \end {gather*}
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 )^2}{(3+2 x)^{5/2}} \, dx &=\int \left (\frac {325}{32 (3+2 x)^{5/2}}-\frac {1065}{32 (3+2 x)^{3/2}}+\frac {651}{16 \sqrt {3+2 x}}-\frac {359}{16} \sqrt {3+2 x}+\frac {165}{32} (3+2 x)^{3/2}-\frac {9}{32} (3+2 x)^{5/2}\right ) \, dx\\ &=-\frac {325}{96 (3+2 x)^{3/2}}+\frac {1065}{32 \sqrt {3+2 x}}+\frac {651}{16} \sqrt {3+2 x}-\frac {359}{48} (3+2 x)^{3/2}+\frac {33}{32} (3+2 x)^{5/2}-\frac {9}{224} (3+2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \begin {gather*} -\frac {27 x^5-144 x^4-215 x^3-1530 x^2-7164 x-7024}{21 (2 x+3)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.05, size = 58, normalized size = 0.73 \begin {gather*} \frac {-27 (2 x+3)^5+693 (2 x+3)^4-5026 (2 x+3)^3+27342 (2 x+3)^2+22365 (2 x+3)-2275}{672 (2 x+3)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 46, normalized size = 0.58 \begin {gather*} -\frac {{\left (27 \, x^{5} - 144 \, x^{4} - 215 \, x^{3} - 1530 \, x^{2} - 7164 \, x - 7024\right )} \sqrt {2 \, x + 3}}{21 \, {\left (4 \, x^{2} + 12 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 51, normalized size = 0.65 \begin {gather*} -\frac {9}{224} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {33}{32} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} - \frac {359}{48} \, {\left (2 \, x + 3\right )}^{\frac {3}{2}} + \frac {651}{16} \, \sqrt {2 \, x + 3} + \frac {5 \, {\left (639 \, x + 926\right )}}{48 \, {\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 = 0.01, size = 35, normalized size = 0.44 \begin {gather*} -\frac {27 x^{5}-144 x^{4}-215 x^{3}-1530 x^{2}-7164 x -7024}{21 \left (2 x +3\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 51, normalized size = 0.65 \begin {gather*} -\frac {9}{224} \, {\left (2 \, x + 3\right )}^{\frac {7}{2}} + \frac {33}{32} \, {\left (2 \, x + 3\right )}^{\frac {5}{2}} - \frac {359}{48} \, {\left (2 \, x + 3\right )}^{\frac {3}{2}} + \frac {651}{16} \, \sqrt {2 \, x + 3} + \frac {5 \, {\left (639 \, x + 926\right )}}{48 \, {\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 = 0.03, size = 50, normalized size = 0.63 \begin {gather*} \frac {\frac {1065\,x}{16}+\frac {2315}{24}}{{\left (2\,x+3\right )}^{3/2}}+\frac {651\,\sqrt {2\,x+3}}{16}-\frac {359\,{\left (2\,x+3\right )}^{3/2}}{48}+\frac {33\,{\left (2\,x+3\right )}^{5/2}}{32}-\frac {9\,{\left (2\,x+3\right )}^{7/2}}{224} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 43.54, size = 70, normalized size = 0.89 \begin {gather*} - \frac {9 \left (2 x + 3\right )^{\frac {7}{2}}}{224} + \frac {33 \left (2 x + 3\right )^{\frac {5}{2}}}{32} - \frac {359 \left (2 x + 3\right )^{\frac {3}{2}}}{48} + \frac {651 \sqrt {2 x + 3}}{16} + \frac {1065}{32 \sqrt {2 x + 3}} - \frac {325}{96 \left (2 x + 3\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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