Optimal. Leaf size=66 \[ -\frac{75}{16} (1-2 x)^{5/2}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{2805}{4} \sqrt{1-2 x}-\frac{8349}{8 \sqrt{1-2 x}}+\frac{9317}{48 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0125482, 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} \[ -\frac{75}{16} (1-2 x)^{5/2}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{2805}{4} \sqrt{1-2 x}-\frac{8349}{8 \sqrt{1-2 x}}+\frac{9317}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{9317}{16 (1-2 x)^{5/2}}-\frac{8349}{8 (1-2 x)^{3/2}}+\frac{2805}{4 \sqrt{1-2 x}}-\frac{1675}{8} \sqrt{1-2 x}+\frac{375}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac{9317}{48 (1-2 x)^{3/2}}-\frac{8349}{8 \sqrt{1-2 x}}-\frac{2805}{4} \sqrt{1-2 x}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{75}{16} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0139388, size = 33, normalized size = 0.5 \[ -\frac{225 x^4+1225 x^3+6240 x^2-13533 x+4457}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{225\,{x}^{4}+1225\,{x}^{3}+6240\,{x}^{2}-13533\,x+4457}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.96033, size = 57, normalized size = 0.86 \begin{align*} -\frac{75}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{1675}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2805}{4} \, \sqrt{-2 \, x + 1} + \frac{121 \,{\left (828 \, x - 337\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54208, size = 119, normalized size = 1.8 \begin{align*} -\frac{{\left (225 \, x^{4} + 1225 \, x^{3} + 6240 \, x^{2} - 13533 \, x + 4457\right )} \sqrt{-2 \, x + 1}}{3 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 15.0144, size = 58, normalized size = 0.88 \begin{align*} - \frac{75 \left (1 - 2 x\right )^{\frac{5}{2}}}{16} + \frac{1675 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} - \frac{2805 \sqrt{1 - 2 x}}{4} - \frac{8349}{8 \sqrt{1 - 2 x}} + \frac{9317}{48 \left (1 - 2 x\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.07256, size = 76, normalized size = 1.15 \begin{align*} -\frac{75}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{1675}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2805}{4} \, \sqrt{-2 \, x + 1} - \frac{121 \,{\left (828 \, x - 337\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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