Optimal. Leaf size=105 \[ \frac{405}{128} (1-2 x)^{15/2}-\frac{97605 (1-2 x)^{13/2}}{1664}+\frac{672003 (1-2 x)^{11/2}}{1408}-\frac{285565}{128} (1-2 x)^{9/2}+\frac{842415}{128} (1-2 x)^{7/2}-\frac{1623419}{128} (1-2 x)^{5/2}+\frac{6206585}{384} (1-2 x)^{3/2}-\frac{2033647}{128} \sqrt{1-2 x} \]
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Rubi [A] time = 0.0184158, antiderivative size = 105, normalized size of antiderivative = 1., 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} \[ \frac{405}{128} (1-2 x)^{15/2}-\frac{97605 (1-2 x)^{13/2}}{1664}+\frac{672003 (1-2 x)^{11/2}}{1408}-\frac{285565}{128} (1-2 x)^{9/2}+\frac{842415}{128} (1-2 x)^{7/2}-\frac{1623419}{128} (1-2 x)^{5/2}+\frac{6206585}{384} (1-2 x)^{3/2}-\frac{2033647}{128} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^2}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{2033647}{128 \sqrt{1-2 x}}-\frac{6206585}{128} \sqrt{1-2 x}+\frac{8117095}{128} (1-2 x)^{3/2}-\frac{5896905}{128} (1-2 x)^{5/2}+\frac{2570085}{128} (1-2 x)^{7/2}-\frac{672003}{128} (1-2 x)^{9/2}+\frac{97605}{128} (1-2 x)^{11/2}-\frac{6075}{128} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{2033647}{128} \sqrt{1-2 x}+\frac{6206585}{384} (1-2 x)^{3/2}-\frac{1623419}{128} (1-2 x)^{5/2}+\frac{842415}{128} (1-2 x)^{7/2}-\frac{285565}{128} (1-2 x)^{9/2}+\frac{672003 (1-2 x)^{11/2}}{1408}-\frac{97605 (1-2 x)^{13/2}}{1664}+\frac{405}{128} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0189129, size = 48, normalized size = 0.46 \[ -\frac{1}{429} \sqrt{1-2 x} \left (173745 x^7+1002375 x^6+2632743 x^5+4212525 x^4+4694340 x^3+4058988 x^2+3152152 x+3275704\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 45, normalized size = 0.4 \begin{align*} -{\frac{173745\,{x}^{7}+1002375\,{x}^{6}+2632743\,{x}^{5}+4212525\,{x}^{4}+4694340\,{x}^{3}+4058988\,{x}^{2}+3152152\,x+3275704}{429}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13129, size = 99, normalized size = 0.94 \begin{align*} \frac{405}{128} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{97605}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{672003}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{285565}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{842415}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1623419}{128} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{6206585}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2033647}{128} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.3, size = 173, normalized size = 1.65 \begin{align*} -\frac{1}{429} \,{\left (173745 \, x^{7} + 1002375 \, x^{6} + 2632743 \, x^{5} + 4212525 \, x^{4} + 4694340 \, x^{3} + 4058988 \, x^{2} + 3152152 \, x + 3275704\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 69.6894, size = 94, normalized size = 0.9 \begin{align*} \frac{405 \left (1 - 2 x\right )^{\frac{15}{2}}}{128} - \frac{97605 \left (1 - 2 x\right )^{\frac{13}{2}}}{1664} + \frac{672003 \left (1 - 2 x\right )^{\frac{11}{2}}}{1408} - \frac{285565 \left (1 - 2 x\right )^{\frac{9}{2}}}{128} + \frac{842415 \left (1 - 2 x\right )^{\frac{7}{2}}}{128} - \frac{1623419 \left (1 - 2 x\right )^{\frac{5}{2}}}{128} + \frac{6206585 \left (1 - 2 x\right )^{\frac{3}{2}}}{384} - \frac{2033647 \sqrt{1 - 2 x}}{128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.31901, size = 155, normalized size = 1.48 \begin{align*} -\frac{405}{128} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} - \frac{97605}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{672003}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{285565}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{842415}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1623419}{128} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{6206585}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2033647}{128} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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