Optimal. Leaf size=92 \[ -\frac {3375 (1-2 x)^{17/2}}{1088}+\frac {765}{16} (1-2 x)^{15/2}-\frac {260055}{832} (1-2 x)^{13/2}+\frac {98209}{88} (1-2 x)^{11/2}-\frac {444983}{192} (1-2 x)^{9/2}+\frac {43197}{16} (1-2 x)^{7/2}-\frac {456533}{320} (1-2 x)^{5/2} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \[ -\frac {3375 (1-2 x)^{17/2}}{1088}+\frac {765}{16} (1-2 x)^{15/2}-\frac {260055}{832} (1-2 x)^{13/2}+\frac {98209}{88} (1-2 x)^{11/2}-\frac {444983}{192} (1-2 x)^{9/2}+\frac {43197}{16} (1-2 x)^{7/2}-\frac {456533}{320} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (\frac {456533}{64} (1-2 x)^{3/2}-\frac {302379}{16} (1-2 x)^{5/2}+\frac {1334949}{64} (1-2 x)^{7/2}-\frac {98209}{8} (1-2 x)^{9/2}+\frac {260055}{64} (1-2 x)^{11/2}-\frac {11475}{16} (1-2 x)^{13/2}+\frac {3375}{64} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {456533}{320} (1-2 x)^{5/2}+\frac {43197}{16} (1-2 x)^{7/2}-\frac {444983}{192} (1-2 x)^{9/2}+\frac {98209}{88} (1-2 x)^{11/2}-\frac {260055}{832} (1-2 x)^{13/2}+\frac {765}{16} (1-2 x)^{15/2}-\frac {3375 (1-2 x)^{17/2}}{1088}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 43, normalized size = 0.47 \[ -\frac {(1-2 x)^{5/2} \left (7239375 x^6+34073325 x^5+70032600 x^4+82215885 x^3+60296725 x^2+27917090 x+7158706\right )}{36465} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 49, normalized size = 0.53 \[ -\frac {1}{36465} \, {\left (28957500 \, x^{8} + 107335800 \, x^{7} + 151076475 \, x^{6} + 82806465 \, x^{5} - 17644040 \, x^{4} - 47302655 \, x^{3} - 22736811 \, x^{2} - 717734 \, x + 7158706\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 113, normalized size = 1.23 \[ -\frac {3375}{1088} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} - \frac {765}{16} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} - \frac {260055}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {98209}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {444983}{192} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {43197}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {456533}{320} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (7239375 x^{6}+34073325 x^{5}+70032600 x^{4}+82215885 x^{3}+60296725 x^{2}+27917090 x +7158706\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{36465} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 64, normalized size = 0.70 \[ -\frac {3375}{1088} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} + \frac {765}{16} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} - \frac {260055}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {98209}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {444983}{192} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {43197}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {456533}{320} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
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 \[ \frac {43197\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {456533\,{\left (1-2\,x\right )}^{5/2}}{320}-\frac {444983\,{\left (1-2\,x\right )}^{9/2}}{192}+\frac {98209\,{\left (1-2\,x\right )}^{11/2}}{88}-\frac {260055\,{\left (1-2\,x\right )}^{13/2}}{832}+\frac {765\,{\left (1-2\,x\right )}^{15/2}}{16}-\frac {3375\,{\left (1-2\,x\right )}^{17/2}}{1088} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.18, size = 82, normalized size = 0.89 \[ - \frac {3375 \left (1 - 2 x\right )^{\frac {17}{2}}}{1088} + \frac {765 \left (1 - 2 x\right )^{\frac {15}{2}}}{16} - \frac {260055 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {98209 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {444983 \left (1 - 2 x\right )^{\frac {9}{2}}}{192} + \frac {43197 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} - \frac {456533 \left (1 - 2 x\right )^{\frac {5}{2}}}{320} \]
Verification of antiderivative is not currently implemented for this CAS.
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