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 = 0.02, 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} \[ -\frac {1}{40} (2 x+3)^{15/2}+\frac {47}{104} (2 x+3)^{13/2}-\frac {109}{88} (2 x+3)^{11/2}+\frac {65}{72} (2 x+3)^{9/2} \]
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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.63, size = 44, normalized size = 0.83 \[ -\frac {1}{6435} \, {\left (20592 \, x^{7} + 30096 \, x^{6} - 447048 \, x^{5} - 2029120 \, x^{4} - 3733305 \, x^{3} - 3496257 \, x^{2} - 1636821 \, x - 301887\right )} \sqrt {2 \, x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 37, normalized size = 0.70 \[ -\frac {1}{40} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {47}{104} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {109}{88} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {65}{72} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} \]
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 \[ -\frac {\left (1287 x^{3}-5841 x^{2}-10269 x -3727\right ) \left (2 x +3\right )^{\frac {9}{2}}}{6435} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 37, normalized size = 0.70 \[ -\frac {1}{40} \, {\left (2 \, x + 3\right )}^{\frac {15}{2}} + \frac {47}{104} \, {\left (2 \, x + 3\right )}^{\frac {13}{2}} - \frac {109}{88} \, {\left (2 \, x + 3\right )}^{\frac {11}{2}} + \frac {65}{72} \, {\left (2 \, x + 3\right )}^{\frac {9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.03, size = 37, normalized size = 0.70 \[ \frac {65\,{\left (2\,x+3\right )}^{9/2}}{72}-\frac {109\,{\left (2\,x+3\right )}^{11/2}}{88}+\frac {47\,{\left (2\,x+3\right )}^{13/2}}{104}-\frac {{\left (2\,x+3\right )}^{15/2}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.78, size = 116, normalized size = 2.19 \[ - \frac {16 x^{7} \sqrt {2 x + 3}}{5} - \frac {304 x^{6} \sqrt {2 x + 3}}{65} + \frac {49672 x^{5} \sqrt {2 x + 3}}{715} + \frac {405824 x^{4} \sqrt {2 x + 3}}{1287} + \frac {248887 x^{3} \sqrt {2 x + 3}}{429} + \frac {388473 x^{2} \sqrt {2 x + 3}}{715} + \frac {181869 x \sqrt {2 x + 3}}{715} + \frac {33543 \sqrt {2 x + 3}}{715} \]
Verification of antiderivative is not currently implemented for this CAS.
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