Optimal. Leaf size=105 \[ \frac {10125 (1-2 x)^{17/2}}{2176}-\frac {10755}{128} (1-2 x)^{15/2}+\frac {1101465 (1-2 x)^{13/2}}{1664}-\frac {4177401 (1-2 x)^{11/2}}{1408}+\frac {9504551 (1-2 x)^{9/2}}{1152}-\frac {1853313}{128} (1-2 x)^{7/2}+\frac {9836211}{640} (1-2 x)^{5/2}-\frac {3195731}{384} (1-2 x)^{3/2} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \[ \frac {10125 (1-2 x)^{17/2}}{2176}-\frac {10755}{128} (1-2 x)^{15/2}+\frac {1101465 (1-2 x)^{13/2}}{1664}-\frac {4177401 (1-2 x)^{11/2}}{1408}+\frac {9504551 (1-2 x)^{9/2}}{1152}-\frac {1853313}{128} (1-2 x)^{7/2}+\frac {9836211}{640} (1-2 x)^{5/2}-\frac {3195731}{384} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (\frac {3195731}{128} \sqrt {1-2 x}-\frac {9836211}{128} (1-2 x)^{3/2}+\frac {12973191}{128} (1-2 x)^{5/2}-\frac {9504551}{128} (1-2 x)^{7/2}+\frac {4177401}{128} (1-2 x)^{9/2}-\frac {1101465}{128} (1-2 x)^{11/2}+\frac {161325}{128} (1-2 x)^{13/2}-\frac {10125}{128} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {3195731}{384} (1-2 x)^{3/2}+\frac {9836211}{640} (1-2 x)^{5/2}-\frac {1853313}{128} (1-2 x)^{7/2}+\frac {9504551 (1-2 x)^{9/2}}{1152}-\frac {4177401 (1-2 x)^{11/2}}{1408}+\frac {1101465 (1-2 x)^{13/2}}{1664}-\frac {10755}{128} (1-2 x)^{15/2}+\frac {10125 (1-2 x)^{17/2}}{2176}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 0.46 \[ -\frac {(1-2 x)^{3/2} \left (65154375 x^7+360231300 x^6+894452625 x^5+1320982290 x^4+1299289000 x^3+906777120 x^2+466679856 x+171312832\right )}{109395} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 49, normalized size = 0.47 \[ \frac {1}{109395} \, {\left (130308750 \, x^{8} + 655308225 \, x^{7} + 1428673950 \, x^{6} + 1747511955 \, x^{5} + 1277595710 \, x^{4} + 514265240 \, x^{3} + 26582592 \, x^{2} - 124054192 \, x - 171312832\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 122, normalized size = 1.16 \[ \frac {10125}{2176} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {10755}{128} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {1101465}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {4177401}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {9504551}{1152} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {1853313}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {9836211}{640} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {3195731}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
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 \[ -\frac {\left (65154375 x^{7}+360231300 x^{6}+894452625 x^{5}+1320982290 x^{4}+1299289000 x^{3}+906777120 x^{2}+466679856 x +171312832\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{109395} \]
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 \[ \frac {10125}{2176} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {10755}{128} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {1101465}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {4177401}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {9504551}{1152} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {1853313}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {9836211}{640} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {3195731}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 73, normalized size = 0.70 \[ \frac {9836211\,{\left (1-2\,x\right )}^{5/2}}{640}-\frac {3195731\,{\left (1-2\,x\right )}^{3/2}}{384}-\frac {1853313\,{\left (1-2\,x\right )}^{7/2}}{128}+\frac {9504551\,{\left (1-2\,x\right )}^{9/2}}{1152}-\frac {4177401\,{\left (1-2\,x\right )}^{11/2}}{1408}+\frac {1101465\,{\left (1-2\,x\right )}^{13/2}}{1664}-\frac {10755\,{\left (1-2\,x\right )}^{15/2}}{128}+\frac {10125\,{\left (1-2\,x\right )}^{17/2}}{2176} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.40, size = 94, normalized size = 0.90 \[ \frac {10125 \left (1 - 2 x\right )^{\frac {17}{2}}}{2176} - \frac {10755 \left (1 - 2 x\right )^{\frac {15}{2}}}{128} + \frac {1101465 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} - \frac {4177401 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} + \frac {9504551 \left (1 - 2 x\right )^{\frac {9}{2}}}{1152} - \frac {1853313 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} + \frac {9836211 \left (1 - 2 x\right )^{\frac {5}{2}}}{640} - \frac {3195731 \left (1 - 2 x\right )^{\frac {3}{2}}}{384} \]
Verification of antiderivative is not currently implemented for this CAS.
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