Optimal. Leaf size=92 \[ -\frac {2025 (1-2 x)^{17/2}}{1088}+\frac {927}{32} (1-2 x)^{15/2}-\frac {159111}{832} (1-2 x)^{13/2}+\frac {121359}{176} (1-2 x)^{11/2}-\frac {832951}{576} (1-2 x)^{9/2}+\frac {54439}{32} (1-2 x)^{7/2}-\frac {290521}{320} (1-2 x)^{5/2} \]
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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} \[ -\frac {2025 (1-2 x)^{17/2}}{1088}+\frac {927}{32} (1-2 x)^{15/2}-\frac {159111}{832} (1-2 x)^{13/2}+\frac {121359}{176} (1-2 x)^{11/2}-\frac {832951}{576} (1-2 x)^{9/2}+\frac {54439}{32} (1-2 x)^{7/2}-\frac {290521}{320} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {290521}{64} (1-2 x)^{3/2}-\frac {381073}{32} (1-2 x)^{5/2}+\frac {832951}{64} (1-2 x)^{7/2}-\frac {121359}{16} (1-2 x)^{9/2}+\frac {159111}{64} (1-2 x)^{11/2}-\frac {13905}{32} (1-2 x)^{13/2}+\frac {2025}{64} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {290521}{320} (1-2 x)^{5/2}+\frac {54439}{32} (1-2 x)^{7/2}-\frac {832951}{576} (1-2 x)^{9/2}+\frac {121359}{176} (1-2 x)^{11/2}-\frac {159111}{832} (1-2 x)^{13/2}+\frac {927}{32} (1-2 x)^{15/2}-\frac {2025 (1-2 x)^{17/2}}{1088}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 0.47 \[ -\frac {(1-2 x)^{5/2} \left (13030875 x^6+62316540 x^5+130072635 x^4+154943820 x^3+115145660 x^2+53902600 x+13931096\right )}{109395} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 49, normalized size = 0.53 \[ -\frac {1}{109395} \, {\left (52123500 \, x^{8} + 197142660 \, x^{7} + 284055255 \, x^{6} + 161801280 \, x^{5} - 29120005 \, x^{4} - 90028420 \, x^{3} - 44740356 \, x^{2} - 1821784 \, x + 13931096\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 113, normalized size = 1.23 \[ -\frac {2025}{1088} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} - \frac {927}{32} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} - \frac {159111}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {121359}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {832951}{576} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {54439}{32} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {290521}{320} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 40, normalized size = 0.43 \[ -\frac {\left (13030875 x^{6}+62316540 x^{5}+130072635 x^{4}+154943820 x^{3}+115145660 x^{2}+53902600 x +13931096\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{109395} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 64, normalized size = 0.70 \[ -\frac {2025}{1088} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} + \frac {927}{32} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} - \frac {159111}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {121359}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {832951}{576} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {54439}{32} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {290521}{320} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
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 \[ \frac {54439\,{\left (1-2\,x\right )}^{7/2}}{32}-\frac {290521\,{\left (1-2\,x\right )}^{5/2}}{320}-\frac {832951\,{\left (1-2\,x\right )}^{9/2}}{576}+\frac {121359\,{\left (1-2\,x\right )}^{11/2}}{176}-\frac {159111\,{\left (1-2\,x\right )}^{13/2}}{832}+\frac {927\,{\left (1-2\,x\right )}^{15/2}}{32}-\frac {2025\,{\left (1-2\,x\right )}^{17/2}}{1088} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.12, size = 82, normalized size = 0.89 \[ - \frac {2025 \left (1 - 2 x\right )^{\frac {17}{2}}}{1088} + \frac {927 \left (1 - 2 x\right )^{\frac {15}{2}}}{32} - \frac {159111 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {121359 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} - \frac {832951 \left (1 - 2 x\right )^{\frac {9}{2}}}{576} + \frac {54439 \left (1 - 2 x\right )^{\frac {7}{2}}}{32} - \frac {290521 \left (1 - 2 x\right )^{\frac {5}{2}}}{320} \]
Verification of antiderivative is not currently implemented for this CAS.
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