Optimal. Leaf size=92 \[ -\frac {1215 (1-2 x)^{17/2}}{1088}+\frac {351}{20} (1-2 x)^{15/2}-\frac {97335}{832} (1-2 x)^{13/2}+\frac {37485}{88} (1-2 x)^{11/2}-\frac {173215}{192} (1-2 x)^{9/2}+\frac {8575}{8} (1-2 x)^{7/2}-\frac {184877}{320} (1-2 x)^{5/2} \]
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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} \[ -\frac {1215 (1-2 x)^{17/2}}{1088}+\frac {351}{20} (1-2 x)^{15/2}-\frac {97335}{832} (1-2 x)^{13/2}+\frac {37485}{88} (1-2 x)^{11/2}-\frac {173215}{192} (1-2 x)^{9/2}+\frac {8575}{8} (1-2 x)^{7/2}-\frac {184877}{320} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^5 (3+5 x) \, dx &=\int \left (\frac {184877}{64} (1-2 x)^{3/2}-\frac {60025}{8} (1-2 x)^{5/2}+\frac {519645}{64} (1-2 x)^{7/2}-\frac {37485}{8} (1-2 x)^{9/2}+\frac {97335}{64} (1-2 x)^{11/2}-\frac {1053}{4} (1-2 x)^{13/2}+\frac {1215}{64} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {184877}{320} (1-2 x)^{5/2}+\frac {8575}{8} (1-2 x)^{7/2}-\frac {173215}{192} (1-2 x)^{9/2}+\frac {37485}{88} (1-2 x)^{11/2}-\frac {97335}{832} (1-2 x)^{13/2}+\frac {351}{20} (1-2 x)^{15/2}-\frac {1215 (1-2 x)^{17/2}}{1088}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 43, normalized size = 0.47 \[ -\frac {(1-2 x)^{5/2} \left (2606175 x^6+12660219 x^5+26832465 x^4+32431860 x^3+24424220 x^2+11562520 x+3012632\right )}{36465} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 49, normalized size = 0.53 \[ -\frac {1}{36465} \, {\left (10424700 \, x^{8} + 40216176 \, x^{7} + 59295159 \, x^{6} + 35057799 \, x^{5} - 5198095 \, x^{4} - 19014940 \, x^{3} - 9775332 \, x^{2} - 488008 \, x + 3012632\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.43, size = 113, normalized size = 1.23 \[ -\frac {1215}{1088} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} - \frac {351}{20} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} - \frac {97335}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {37485}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {173215}{192} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {8575}{8} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {184877}{320} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (2606175 x^{6}+12660219 x^{5}+26832465 x^{4}+32431860 x^{3}+24424220 x^{2}+11562520 x +3012632\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{36465} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 64, normalized size = 0.70 \[ -\frac {1215}{1088} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} + \frac {351}{20} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} - \frac {97335}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {37485}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {173215}{192} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {8575}{8} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {184877}{320} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
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 \[ \frac {8575\,{\left (1-2\,x\right )}^{7/2}}{8}-\frac {184877\,{\left (1-2\,x\right )}^{5/2}}{320}-\frac {173215\,{\left (1-2\,x\right )}^{9/2}}{192}+\frac {37485\,{\left (1-2\,x\right )}^{11/2}}{88}-\frac {97335\,{\left (1-2\,x\right )}^{13/2}}{832}+\frac {351\,{\left (1-2\,x\right )}^{15/2}}{20}-\frac {1215\,{\left (1-2\,x\right )}^{17/2}}{1088} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.19, size = 82, normalized size = 0.89 \[ - \frac {1215 \left (1 - 2 x\right )^{\frac {17}{2}}}{1088} + \frac {351 \left (1 - 2 x\right )^{\frac {15}{2}}}{20} - \frac {97335 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {37485 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {173215 \left (1 - 2 x\right )^{\frac {9}{2}}}{192} + \frac {8575 \left (1 - 2 x\right )^{\frac {7}{2}}}{8} - \frac {184877 \left (1 - 2 x\right )^{\frac {5}{2}}}{320} \]
Verification of antiderivative is not currently implemented for this CAS.
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