Optimal. Leaf size=66 \[ -\frac {375}{176} (1-2 x)^{11/2}+\frac {1675}{72} (1-2 x)^{9/2}-\frac {2805}{28} (1-2 x)^{7/2}+\frac {8349}{40} (1-2 x)^{5/2}-\frac {9317}{48} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.01, antiderivative size = 66, 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} \begin {gather*} -\frac {375}{176} (1-2 x)^{11/2}+\frac {1675}{72} (1-2 x)^{9/2}-\frac {2805}{28} (1-2 x)^{7/2}+\frac {8349}{40} (1-2 x)^{5/2}-\frac {9317}{48} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac {9317}{16} \sqrt {1-2 x}-\frac {8349}{8} (1-2 x)^{3/2}+\frac {2805}{4} (1-2 x)^{5/2}-\frac {1675}{8} (1-2 x)^{7/2}+\frac {375}{16} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {9317}{48} (1-2 x)^{3/2}+\frac {8349}{40} (1-2 x)^{5/2}-\frac {2805}{28} (1-2 x)^{7/2}+\frac {1675}{72} (1-2 x)^{9/2}-\frac {375}{176} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {(1-2 x)^{3/2} \left (118125 x^4+408625 x^3+598350 x^2+482583 x+223231\right )}{3465} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 60, normalized size = 0.91 \begin {gather*} \frac {-118125 (1-2 x)^{11/2}+1289750 (1-2 x)^{9/2}-5553900 (1-2 x)^{7/2}+11571714 (1-2 x)^{5/2}-10761135 (1-2 x)^{3/2}}{55440} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.73, size = 34, normalized size = 0.52 \begin {gather*} \frac {1}{3465} \, {\left (236250 \, x^{5} + 699125 \, x^{4} + 788075 \, x^{3} + 366816 \, x^{2} - 36121 \, x - 223231\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.31, size = 74, normalized size = 1.12 \begin {gather*} \frac {375}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1675}{72} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {2805}{28} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {8349}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {9317}{48} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \begin {gather*} -\frac {\left (118125 x^{4}+408625 x^{3}+598350 x^{2}+482583 x +223231\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{3465} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 46, normalized size = 0.70 \begin {gather*} -\frac {375}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1675}{72} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {2805}{28} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {8349}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {9317}{48} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 46, normalized size = 0.70 \begin {gather*} \frac {8349\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {9317\,{\left (1-2\,x\right )}^{3/2}}{48}-\frac {2805\,{\left (1-2\,x\right )}^{7/2}}{28}+\frac {1675\,{\left (1-2\,x\right )}^{9/2}}{72}-\frac {375\,{\left (1-2\,x\right )}^{11/2}}{176} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.59, size = 58, normalized size = 0.88 \begin {gather*} - \frac {375 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} + \frac {1675 \left (1 - 2 x\right )^{\frac {9}{2}}}{72} - \frac {2805 \left (1 - 2 x\right )^{\frac {7}{2}}}{28} + \frac {8349 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {9317 \left (1 - 2 x\right )^{\frac {3}{2}}}{48} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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