Optimal. Leaf size=79 \[ \frac {1125}{544} (1-2 x)^{17/2}-\frac {845}{32} (1-2 x)^{15/2}+\frac {28555}{208} (1-2 x)^{13/2}-\frac {5847}{16} (1-2 x)^{11/2}+\frac {16093}{32} (1-2 x)^{9/2}-\frac {9317}{32} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.02, antiderivative size = 79, 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} \[ \frac {1125}{544} (1-2 x)^{17/2}-\frac {845}{32} (1-2 x)^{15/2}+\frac {28555}{208} (1-2 x)^{13/2}-\frac {5847}{16} (1-2 x)^{11/2}+\frac {16093}{32} (1-2 x)^{9/2}-\frac {9317}{32} (1-2 x)^{7/2} \]
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)^3 \, dx &=\int \left (\frac {65219}{32} (1-2 x)^{5/2}-\frac {144837}{32} (1-2 x)^{7/2}+\frac {64317}{16} (1-2 x)^{9/2}-\frac {28555}{16} (1-2 x)^{11/2}+\frac {12675}{32} (1-2 x)^{13/2}-\frac {1125}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {9317}{32} (1-2 x)^{7/2}+\frac {16093}{32} (1-2 x)^{9/2}-\frac {5847}{16} (1-2 x)^{11/2}+\frac {28555}{208} (1-2 x)^{13/2}-\frac {845}{32} (1-2 x)^{15/2}+\frac {1125}{544} (1-2 x)^{17/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 0.48 \[ -\frac {1}{221} (1-2 x)^{7/2} \left (14625 x^5+56810 x^4+92535 x^3+80748 x^2+39160 x+9004\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 49, normalized size = 0.62 \[ \frac {1}{221} \, {\left (117000 \, x^{8} + 278980 \, x^{7} + 146310 \, x^{6} - 138201 \, x^{5} - 157296 \, x^{4} - 5935 \, x^{3} + 46164 \, x^{2} + 14864 \, x - 9004\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 97, normalized size = 1.23 \[ \frac {1125}{544} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {845}{32} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {28555}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {5847}{16} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {16093}{32} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {9317}{32} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.44 \[ -\frac {\left (14625 x^{5}+56810 x^{4}+92535 x^{3}+80748 x^{2}+39160 x +9004\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{221} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 55, normalized size = 0.70 \[ \frac {1125}{544} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {845}{32} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {28555}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {5847}{16} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {16093}{32} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {9317}{32} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 55, normalized size = 0.70 \[ \frac {16093\,{\left (1-2\,x\right )}^{9/2}}{32}-\frac {9317\,{\left (1-2\,x\right )}^{7/2}}{32}-\frac {5847\,{\left (1-2\,x\right )}^{11/2}}{16}+\frac {28555\,{\left (1-2\,x\right )}^{13/2}}{208}-\frac {845\,{\left (1-2\,x\right )}^{15/2}}{32}+\frac {1125\,{\left (1-2\,x\right )}^{17/2}}{544} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 20.85, size = 70, normalized size = 0.89 \[ \frac {1125 \left (1 - 2 x\right )^{\frac {17}{2}}}{544} - \frac {845 \left (1 - 2 x\right )^{\frac {15}{2}}}{32} + \frac {28555 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} - \frac {5847 \left (1 - 2 x\right )^{\frac {11}{2}}}{16} + \frac {16093 \left (1 - 2 x\right )^{\frac {9}{2}}}{32} - \frac {9317 \left (1 - 2 x\right )^{\frac {7}{2}}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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