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 = 0.02, antiderivative size = 92, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.87, size = 46, normalized size = 0.50 \[ \frac {{\left (1215 \, x^{6} + 6651 \, x^{5} + 17055 \, x^{4} + 28692 \, x^{3} + 41012 \, x^{2} + 91704 \, x - 92760\right )} \sqrt {-2 \, x + 1}}{11 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 92, normalized size = 1.00 \[ \frac {1215}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {117}{4} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {13905}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {7497}{8} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {173215}{64} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {60025}{8} \, \sqrt {-2 \, x + 1} + \frac {184877}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {1215 x^{6}+6651 x^{5}+17055 x^{4}+28692 x^{3}+41012 x^{2}+91704 x -92760}{11 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 64, normalized size = 0.70 \[ -\frac {1215}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {117}{4} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {13905}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {7497}{8} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {173215}{64} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {60025}{8} \, \sqrt {-2 \, x + 1} + \frac {184877}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {184877}{64\,\sqrt {1-2\,x}}+\frac {60025\,\sqrt {1-2\,x}}{8}-\frac {173215\,{\left (1-2\,x\right )}^{3/2}}{64}+\frac {7497\,{\left (1-2\,x\right )}^{5/2}}{8}-\frac {13905\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {117\,{\left (1-2\,x\right )}^{9/2}}{4}-\frac {1215\,{\left (1-2\,x\right )}^{11/2}}{704} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 42.54, size = 82, normalized size = 0.89 \[ - \frac {1215 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {117 \left (1 - 2 x\right )^{\frac {9}{2}}}{4} - \frac {13905 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {7497 \left (1 - 2 x\right )^{\frac {5}{2}}}{8} - \frac {173215 \left (1 - 2 x\right )^{\frac {3}{2}}}{64} + \frac {60025 \sqrt {1 - 2 x}}{8} + \frac {184877}{64 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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