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 = 0.0116112, antiderivative size = 66, normalized size of antiderivative = 1., 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} \[ -\frac{125}{48} (1-2 x)^{9/2}+\frac{1675}{56} (1-2 x)^{7/2}-\frac{561}{4} (1-2 x)^{5/2}+\frac{2783}{8} (1-2 x)^{3/2}-\frac{9317}{16} \sqrt{1-2 x} \]
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*}
Mathematica [A] time = 0.0115998, size = 33, normalized size = 0.5 \[ -\frac{1}{21} \sqrt{1-2 x} \left (875 x^4+3275 x^3+5556 x^2+6161 x+7295\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{875\,{x}^{4}+3275\,{x}^{3}+5556\,{x}^{2}+6161\,x+7295}{21}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.89769, size = 62, normalized size = 0.94 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57697, size = 95, normalized size = 1.44 \begin{align*} -\frac{1}{21} \,{\left (875 \, x^{4} + 3275 \, x^{3} + 5556 \, x^{2} + 6161 \, x + 7295\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 30.0102, size = 58, normalized size = 0.88 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.9422, size = 90, normalized size = 1.36 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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