Optimal. Leaf size=92 \[ -\frac{1215}{704} (1-2 x)^{11/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{60025}{8} \sqrt{1-2 x}+\frac{184877}{64 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0158934, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {77} \[ -\frac{1215}{704} (1-2 x)^{11/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{60025}{8} \sqrt{1-2 x}+\frac{184877}{64 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{184877}{64 (1-2 x)^{3/2}}-\frac{60025}{8 \sqrt{1-2 x}}+\frac{519645}{64} \sqrt{1-2 x}-\frac{37485}{8} (1-2 x)^{3/2}+\frac{97335}{64} (1-2 x)^{5/2}-\frac{1053}{4} (1-2 x)^{7/2}+\frac{1215}{64} (1-2 x)^{9/2}\right ) \, dx\\ &=\frac{184877}{64 \sqrt{1-2 x}}+\frac{60025}{8} \sqrt{1-2 x}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{1215}{704} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0160357, size = 43, normalized size = 0.47 \[ \frac{-1215 x^6-6651 x^5-17055 x^4-28692 x^3-41012 x^2-91704 x+92760}{11 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 40, normalized size = 0.4 \begin{align*} -{\frac{1215\,{x}^{6}+6651\,{x}^{5}+17055\,{x}^{4}+28692\,{x}^{3}+41012\,{x}^{2}+91704\,x-92760}{11}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.46058, size = 86, normalized size = 0.93 \begin{align*} -\frac{1215}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{117}{4} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{13905}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{7497}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{173215}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{60025}{8} \, \sqrt{-2 \, x + 1} + \frac{184877}{64 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60454, size = 144, normalized size = 1.57 \begin{align*} \frac{{\left (1215 \, x^{6} + 6651 \, x^{5} + 17055 \, x^{4} + 28692 \, x^{3} + 41012 \, x^{2} + 91704 \, x - 92760\right )} \sqrt{-2 \, x + 1}}{11 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 29.0217, size = 82, normalized size = 0.89 \begin{align*} - \frac{1215 \left (1 - 2 x\right )^{\frac{11}{2}}}{704} + \frac{117 \left (1 - 2 x\right )^{\frac{9}{2}}}{4} - \frac{13905 \left (1 - 2 x\right )^{\frac{7}{2}}}{64} + \frac{7497 \left (1 - 2 x\right )^{\frac{5}{2}}}{8} - \frac{173215 \left (1 - 2 x\right )^{\frac{3}{2}}}{64} + \frac{60025 \sqrt{1 - 2 x}}{8} + \frac{184877}{64 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20078, size = 124, normalized size = 1.35 \begin{align*} \frac{1215}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{117}{4} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{13905}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{7497}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{173215}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{60025}{8} \, \sqrt{-2 \, x + 1} + \frac{184877}{64 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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