Optimal. Leaf size=66 \[ -\frac {25}{16} (1-2 x)^{15/2}+\frac {1675}{104} (1-2 x)^{13/2}-\frac {255}{4} (1-2 x)^{11/2}+\frac {2783}{24} (1-2 x)^{9/2}-\frac {1331}{16} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.01, antiderivative size = 66, 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} \[ -\frac {25}{16} (1-2 x)^{15/2}+\frac {1675}{104} (1-2 x)^{13/2}-\frac {255}{4} (1-2 x)^{11/2}+\frac {2783}{24} (1-2 x)^{9/2}-\frac {1331}{16} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac {9317}{16} (1-2 x)^{5/2}-\frac {8349}{8} (1-2 x)^{7/2}+\frac {2805}{4} (1-2 x)^{9/2}-\frac {1675}{8} (1-2 x)^{11/2}+\frac {375}{16} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {1331}{16} (1-2 x)^{7/2}+\frac {2783}{24} (1-2 x)^{9/2}-\frac {255}{4} (1-2 x)^{11/2}+\frac {1675}{104} (1-2 x)^{13/2}-\frac {25}{16} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {1}{39} (1-2 x)^{7/2} \left (975 x^4+3075 x^3+3870 x^2+2381 x+641\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 44, normalized size = 0.67 \[ \frac {1}{39} \, {\left (7800 \, x^{7} + 12900 \, x^{6} - 90 \, x^{5} - 9917 \, x^{4} - 3299 \, x^{3} + 2724 \, x^{2} + 1465 \, x - 641\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 81, normalized size = 1.23 \[ \frac {25}{16} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {1675}{104} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {255}{4} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {2783}{24} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {1331}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \[ -\frac {\left (975 x^{4}+3075 x^{3}+3870 x^{2}+2381 x +641\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{39} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 46, normalized size = 0.70 \[ -\frac {25}{16} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {1675}{104} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {255}{4} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {2783}{24} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {1331}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 46, normalized size = 0.70 \[ \frac {2783\,{\left (1-2\,x\right )}^{9/2}}{24}-\frac {1331\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {255\,{\left (1-2\,x\right )}^{11/2}}{4}+\frac {1675\,{\left (1-2\,x\right )}^{13/2}}{104}-\frac {25\,{\left (1-2\,x\right )}^{15/2}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 16.93, size = 58, normalized size = 0.88 \[ - \frac {25 \left (1 - 2 x\right )^{\frac {15}{2}}}{16} + \frac {1675 \left (1 - 2 x\right )^{\frac {13}{2}}}{104} - \frac {255 \left (1 - 2 x\right )^{\frac {11}{2}}}{4} + \frac {2783 \left (1 - 2 x\right )^{\frac {9}{2}}}{24} - \frac {1331 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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