Optimal. Leaf size=79 \[ \frac {675}{544} (1-2 x)^{17/2}-\frac {513}{32} (1-2 x)^{15/2}+\frac {17541}{208} (1-2 x)^{13/2}-\frac {39977}{176} (1-2 x)^{11/2}+\frac {91091}{288} (1-2 x)^{9/2}-\frac {5929}{32} (1-2 x)^{7/2} \]
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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} \[ \frac {675}{544} (1-2 x)^{17/2}-\frac {513}{32} (1-2 x)^{15/2}+\frac {17541}{208} (1-2 x)^{13/2}-\frac {39977}{176} (1-2 x)^{11/2}+\frac {91091}{288} (1-2 x)^{9/2}-\frac {5929}{32} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (\frac {41503}{32} (1-2 x)^{5/2}-\frac {91091}{32} (1-2 x)^{7/2}+\frac {39977}{16} (1-2 x)^{9/2}-\frac {17541}{16} (1-2 x)^{11/2}+\frac {7695}{32} (1-2 x)^{13/2}-\frac {675}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {5929}{32} (1-2 x)^{7/2}+\frac {91091}{288} (1-2 x)^{9/2}-\frac {39977}{176} (1-2 x)^{11/2}+\frac {17541}{208} (1-2 x)^{13/2}-\frac {513}{32} (1-2 x)^{15/2}+\frac {675}{544} (1-2 x)^{17/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 0.48 \[ -\frac {(1-2 x)^{7/2} \left (868725 x^5+3440151 x^4+5708637 x^3+5069475 x^2+2497634 x+581846\right )}{21879} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 49, normalized size = 0.62 \[ \frac {1}{21879} \, {\left (6949800 \, x^{8} + 17096508 \, x^{7} + 9599634 \, x^{6} - 8175663 \, x^{5} - 10040957 \, x^{4} - 608627 \, x^{3} + 2934177 \, x^{2} + 993442 \, x - 581846\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 97, normalized size = 1.23 \[ \frac {675}{544} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {513}{32} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {17541}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {39977}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {91091}{288} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {5929}{32} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (868725 x^{5}+3440151 x^{4}+5708637 x^{3}+5069475 x^{2}+2497634 x +581846\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{21879} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 55, normalized size = 0.70 \[ \frac {675}{544} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {513}{32} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {17541}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {39977}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {91091}{288} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {5929}{32} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
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 \[ \frac {91091\,{\left (1-2\,x\right )}^{9/2}}{288}-\frac {5929\,{\left (1-2\,x\right )}^{7/2}}{32}-\frac {39977\,{\left (1-2\,x\right )}^{11/2}}{176}+\frac {17541\,{\left (1-2\,x\right )}^{13/2}}{208}-\frac {513\,{\left (1-2\,x\right )}^{15/2}}{32}+\frac {675\,{\left (1-2\,x\right )}^{17/2}}{544} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.02, size = 70, normalized size = 0.89 \[ \frac {675 \left (1 - 2 x\right )^{\frac {17}{2}}}{544} - \frac {513 \left (1 - 2 x\right )^{\frac {15}{2}}}{32} + \frac {17541 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} - \frac {39977 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} + \frac {91091 \left (1 - 2 x\right )^{\frac {9}{2}}}{288} - \frac {5929 \left (1 - 2 x\right )^{\frac {7}{2}}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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