Optimal. Leaf size=66 \[ -\frac {125}{48} (1-2 x)^{9/2}+\frac {1675}{56} (1-2 x)^{7/2}-\frac {561}{4} (1-2 x)^{5/2}+\frac {2783}{8} (1-2 x)^{3/2}-\frac {9317}{16} \sqrt {1-2 x} \]
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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 {125}{48} (1-2 x)^{9/2}+\frac {1675}{56} (1-2 x)^{7/2}-\frac {561}{4} (1-2 x)^{5/2}+\frac {2783}{8} (1-2 x)^{3/2}-\frac {9317}{16} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^3}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {9317}{16 \sqrt {1-2 x}}-\frac {8349}{8} \sqrt {1-2 x}+\frac {2805}{4} (1-2 x)^{3/2}-\frac {1675}{8} (1-2 x)^{5/2}+\frac {375}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {9317}{16} \sqrt {1-2 x}+\frac {2783}{8} (1-2 x)^{3/2}-\frac {561}{4} (1-2 x)^{5/2}+\frac {1675}{56} (1-2 x)^{7/2}-\frac {125}{48} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {1}{21} \sqrt {1-2 x} \left (875 x^4+3275 x^3+5556 x^2+6161 x+7295\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 49, normalized size = 0.74 \begin {gather*} -\frac {1}{336} \left (875 (1-2 x)^4-10050 (1-2 x)^3+47124 (1-2 x)^2-116886 (1-2 x)+195657\right ) \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.12, size = 29, normalized size = 0.44 \begin {gather*} -\frac {1}{21} \, {\left (875 \, x^{4} + 3275 \, x^{3} + 5556 \, x^{2} + 6161 \, x + 7295\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 67, normalized size = 1.02 \begin {gather*} -\frac {125}{48} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {1675}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {561}{4} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {2783}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {9317}{16} \, \sqrt {-2 \, x + 1} \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 (875 x^{4}+3275 x^{3}+5556 x^{2}+6161 x +7295\right ) \sqrt {-2 x +1}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 46, normalized size = 0.70 \begin {gather*} -\frac {125}{48} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {1675}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {561}{4} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {2783}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {9317}{16} \, \sqrt {-2 \, x + 1} \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 {2783\,{\left (1-2\,x\right )}^{3/2}}{8}-\frac {9317\,\sqrt {1-2\,x}}{16}-\frac {561\,{\left (1-2\,x\right )}^{5/2}}{4}+\frac {1675\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {125\,{\left (1-2\,x\right )}^{9/2}}{48} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 42.90, size = 58, normalized size = 0.88 \begin {gather*} - \frac {125 \left (1 - 2 x\right )^{\frac {9}{2}}}{48} + \frac {1675 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {561 \left (1 - 2 x\right )^{\frac {5}{2}}}{4} + \frac {2783 \left (1 - 2 x\right )^{\frac {3}{2}}}{8} - \frac {9317 \sqrt {1 - 2 x}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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