Optimal. Leaf size=105 \[ \frac {3645 (1-2 x)^{19/2}}{2432}-\frac {59049 (1-2 x)^{17/2}}{2176}+\frac {136647}{640} (1-2 x)^{15/2}-\frac {1580985 (1-2 x)^{13/2}}{1664}+\frac {3658095 (1-2 x)^{11/2}}{1408}-\frac {564235}{128} (1-2 x)^{9/2}+\frac {559433}{128} (1-2 x)^{7/2}-\frac {1294139}{640} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.02, antiderivative size = 105, 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} \[ \frac {3645 (1-2 x)^{19/2}}{2432}-\frac {59049 (1-2 x)^{17/2}}{2176}+\frac {136647}{640} (1-2 x)^{15/2}-\frac {1580985 (1-2 x)^{13/2}}{1664}+\frac {3658095 (1-2 x)^{11/2}}{1408}-\frac {564235}{128} (1-2 x)^{9/2}+\frac {559433}{128} (1-2 x)^{7/2}-\frac {1294139}{640} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^6 (3+5 x) \, dx &=\int \left (\frac {1294139}{128} (1-2 x)^{3/2}-\frac {3916031}{128} (1-2 x)^{5/2}+\frac {5078115}{128} (1-2 x)^{7/2}-\frac {3658095}{128} (1-2 x)^{9/2}+\frac {1580985}{128} (1-2 x)^{11/2}-\frac {409941}{128} (1-2 x)^{13/2}+\frac {59049}{128} (1-2 x)^{15/2}-\frac {3645}{128} (1-2 x)^{17/2}\right ) \, dx\\ &=-\frac {1294139}{640} (1-2 x)^{5/2}+\frac {559433}{128} (1-2 x)^{7/2}-\frac {564235}{128} (1-2 x)^{9/2}+\frac {3658095 (1-2 x)^{11/2}}{1408}-\frac {1580985 (1-2 x)^{13/2}}{1664}+\frac {136647}{640} (1-2 x)^{15/2}-\frac {59049 (1-2 x)^{17/2}}{2176}+\frac {3645 (1-2 x)^{19/2}}{2432}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 0.46 \[ -\frac {(1-2 x)^{5/2} \left (44304975 x^7+246022920 x^6+607227192 x^5+876286620 x^4+817490880 x^3+512679760 x^2+214047840 x+51677856\right )}{230945} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 54, normalized size = 0.51 \[ -\frac {1}{230945} \, {\left (177219900 \, x^{9} + 806871780 \, x^{8} + 1489122063 \, x^{7} + 1322260632 \, x^{6} + 372044232 \, x^{5} - 342957860 \, x^{4} - 377036800 \, x^{3} - 136800176 \, x^{2} + 7336416 \, x + 51677856\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.30, size = 129, normalized size = 1.23 \[ -\frac {3645}{2432} \, {\left (2 \, x - 1\right )}^{9} \sqrt {-2 \, x + 1} - \frac {59049}{2176} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} - \frac {136647}{640} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} - \frac {1580985}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {3658095}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {564235}{128} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {559433}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {1294139}{640} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 0.43 \[ -\frac {\left (44304975 x^{7}+246022920 x^{6}+607227192 x^{5}+876286620 x^{4}+817490880 x^{3}+512679760 x^{2}+214047840 x +51677856\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{230945} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 73, normalized size = 0.70 \[ \frac {3645}{2432} \, {\left (-2 \, x + 1\right )}^{\frac {19}{2}} - \frac {59049}{2176} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} + \frac {136647}{640} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} - \frac {1580985}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {3658095}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {564235}{128} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {559433}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {1294139}{640} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 73, normalized size = 0.70 \[ \frac {559433\,{\left (1-2\,x\right )}^{7/2}}{128}-\frac {1294139\,{\left (1-2\,x\right )}^{5/2}}{640}-\frac {564235\,{\left (1-2\,x\right )}^{9/2}}{128}+\frac {3658095\,{\left (1-2\,x\right )}^{11/2}}{1408}-\frac {1580985\,{\left (1-2\,x\right )}^{13/2}}{1664}+\frac {136647\,{\left (1-2\,x\right )}^{15/2}}{640}-\frac {59049\,{\left (1-2\,x\right )}^{17/2}}{2176}+\frac {3645\,{\left (1-2\,x\right )}^{19/2}}{2432} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 25.83, size = 94, normalized size = 0.90 \[ \frac {3645 \left (1 - 2 x\right )^{\frac {19}{2}}}{2432} - \frac {59049 \left (1 - 2 x\right )^{\frac {17}{2}}}{2176} + \frac {136647 \left (1 - 2 x\right )^{\frac {15}{2}}}{640} - \frac {1580985 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} + \frac {3658095 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} - \frac {564235 \left (1 - 2 x\right )^{\frac {9}{2}}}{128} + \frac {559433 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} - \frac {1294139 \left (1 - 2 x\right )^{\frac {5}{2}}}{640} \]
Verification of antiderivative is not currently implemented for this CAS.
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