Optimal. Leaf size=92 \[ \frac {184877}{64 \sqrt {1-2 x}}+\frac {60025}{8} \sqrt {1-2 x}-\frac {173215}{64} (1-2 x)^{3/2}+\frac {7497}{8} (1-2 x)^{5/2}-\frac {13905}{64} (1-2 x)^{7/2}+\frac {117}{4} (1-2 x)^{9/2}-\frac {1215}{704} (1-2 x)^{11/2} \]
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Rubi [A]
time = 0.01, 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 = {78}
\begin {gather*} -\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}} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
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 \begin {gather*} \frac {92760-91704 x-41012 x^2-28692 x^3-17055 x^4-6651 x^5-1215 x^6}{11 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 65, normalized size = 0.71
method | result | size |
gosper | \(-\frac {1215 x^{6}+6651 x^{5}+17055 x^{4}+28692 x^{3}+41012 x^{2}+91704 x -92760}{11 \sqrt {1-2 x}}\) | \(40\) |
risch | \(-\frac {1215 x^{6}+6651 x^{5}+17055 x^{4}+28692 x^{3}+41012 x^{2}+91704 x -92760}{11 \sqrt {1-2 x}}\) | \(40\) |
trager | \(\frac {\left (1215 x^{6}+6651 x^{5}+17055 x^{4}+28692 x^{3}+41012 x^{2}+91704 x -92760\right ) \sqrt {1-2 x}}{-11+22 x}\) | \(47\) |
derivativedivides | \(-\frac {173215 \left (1-2 x \right )^{\frac {3}{2}}}{64}+\frac {7497 \left (1-2 x \right )^{\frac {5}{2}}}{8}-\frac {13905 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {117 \left (1-2 x \right )^{\frac {9}{2}}}{4}-\frac {1215 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {184877}{64 \sqrt {1-2 x}}+\frac {60025 \sqrt {1-2 x}}{8}\) | \(65\) |
default | \(-\frac {173215 \left (1-2 x \right )^{\frac {3}{2}}}{64}+\frac {7497 \left (1-2 x \right )^{\frac {5}{2}}}{8}-\frac {13905 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {117 \left (1-2 x \right )^{\frac {9}{2}}}{4}-\frac {1215 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {184877}{64 \sqrt {1-2 x}}+\frac {60025 \sqrt {1-2 x}}{8}\) | \(65\) |
meijerg | \(-\frac {96 \left (\sqrt {\pi }-\frac {\sqrt {\pi }}{\sqrt {1-2 x}}\right )}{\sqrt {\pi }}+\frac {-880 \sqrt {\pi }+\frac {110 \sqrt {\pi }\, \left (-8 x +8\right )}{\sqrt {1-2 x}}}{\sqrt {\pi }}-\frac {840 \left (\frac {8 \sqrt {\pi }}{3}-\frac {\sqrt {\pi }\, \left (-8 x^{2}-16 x +16\right )}{6 \sqrt {1-2 x}}\right )}{\sqrt {\pi }}+\frac {-2736 \sqrt {\pi }+\frac {171 \sqrt {\pi }\, \left (-64 x^{3}-64 x^{2}-128 x +128\right )}{8 \sqrt {1-2 x}}}{\sqrt {\pi }}-\frac {3915 \left (\frac {128 \sqrt {\pi }}{35}-\frac {\sqrt {\pi }\, \left (-160 x^{4}-128 x^{3}-128 x^{2}-256 x +256\right )}{70 \sqrt {1-2 x}}\right )}{8 \sqrt {\pi }}+\frac {-\frac {4248 \sqrt {\pi }}{7}+\frac {531 \sqrt {\pi }\, \left (-896 x^{5}-640 x^{4}-512 x^{3}-512 x^{2}-1024 x +1024\right )}{896 \sqrt {1-2 x}}}{\sqrt {\pi }}-\frac {1215 \left (\frac {1024 \sqrt {\pi }}{231}-\frac {\sqrt {\pi }\, \left (-2688 x^{6}-1792 x^{5}-1280 x^{4}-1024 x^{3}-1024 x^{2}-2048 x +2048\right )}{462 \sqrt {1-2 x}}\right )}{64 \sqrt {\pi }}\) | \(266\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 64, normalized size = 0.70 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.83, size = 46, normalized size = 0.50 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 21.49, size = 82, normalized size = 0.89 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.00, size = 92, normalized size = 1.00 \begin {gather*} \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 {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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