Optimal. Leaf size=66 \[ -\frac {15}{16} (1-2 x)^{15/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {847}{16} (1-2 x)^{7/2} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \[ -\frac {15}{16} (1-2 x)^{15/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {847}{16} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (\frac {5929}{16} (1-2 x)^{5/2}-\frac {1309}{2} (1-2 x)^{7/2}+\frac {3467}{8} (1-2 x)^{9/2}-\frac {255}{2} (1-2 x)^{11/2}+\frac {225}{16} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {847}{16} (1-2 x)^{7/2}+\frac {1309}{18} (1-2 x)^{9/2}-\frac {3467}{88} (1-2 x)^{11/2}+\frac {255}{26} (1-2 x)^{13/2}-\frac {15}{16} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {(1-2 x)^{7/2} \left (19305 x^4+62370 x^3+80307 x^2+50450 x+13826\right )}{1287} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 44, normalized size = 0.67 \[ \frac {1}{1287} \, {\left (154440 \, x^{7} + 267300 \, x^{6} + 9846 \, x^{5} - 205169 \, x^{4} - 75320 \, x^{3} + 56481 \, x^{2} + 32506 \, x - 13826\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 81, normalized size = 1.23 \[ \frac {15}{16} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {255}{26} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {3467}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1309}{18} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {847}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (19305 x^{4}+62370 x^{3}+80307 x^{2}+50450 x +13826\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{1287} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 46, normalized size = 0.70 \[ -\frac {15}{16} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {255}{26} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {3467}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1309}{18} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {847}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 46, normalized size = 0.70 \[ \frac {1309\,{\left (1-2\,x\right )}^{9/2}}{18}-\frac {847\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {3467\,{\left (1-2\,x\right )}^{11/2}}{88}+\frac {255\,{\left (1-2\,x\right )}^{13/2}}{26}-\frac {15\,{\left (1-2\,x\right )}^{15/2}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 17.42, size = 58, normalized size = 0.88 \[ - \frac {15 \left (1 - 2 x\right )^{\frac {15}{2}}}{16} + \frac {255 \left (1 - 2 x\right )^{\frac {13}{2}}}{26} - \frac {3467 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} + \frac {1309 \left (1 - 2 x\right )^{\frac {9}{2}}}{18} - \frac {847 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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