Optimal. Leaf size=66 \[ -\frac{45}{16} (1-2 x)^{5/2}+\frac{85}{2} (1-2 x)^{3/2}-\frac{3467}{8} \sqrt{1-2 x}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{5929}{48 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0134463, antiderivative size = 66, 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} \[ -\frac{45}{16} (1-2 x)^{5/2}+\frac{85}{2} (1-2 x)^{3/2}-\frac{3467}{8} \sqrt{1-2 x}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{5929}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{5929}{16 (1-2 x)^{5/2}}-\frac{1309}{2 (1-2 x)^{3/2}}+\frac{3467}{8 \sqrt{1-2 x}}-\frac{255}{2} \sqrt{1-2 x}+\frac{225}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac{5929}{48 (1-2 x)^{3/2}}-\frac{1309}{2 \sqrt{1-2 x}}-\frac{3467}{8} \sqrt{1-2 x}+\frac{85}{2} (1-2 x)^{3/2}-\frac{45}{16} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0131909, size = 33, normalized size = 0.5 \[ -\frac{135 x^4+750 x^3+3873 x^2-8430 x+2774}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 30, normalized size = 0.5 \begin{align*} -{\frac{135\,{x}^{4}+750\,{x}^{3}+3873\,{x}^{2}-8430\,x+2774}{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 = 1.70428, size = 57, normalized size = 0.86 \begin{align*} -\frac{45}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{85}{2} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3467}{8} \, \sqrt{-2 \, x + 1} + \frac{77 \,{\left (816 \, x - 331\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 = 1.53527, size = 116, normalized size = 1.76 \begin{align*} -\frac{{\left (135 \, x^{4} + 750 \, x^{3} + 3873 \, x^{2} - 8430 \, x + 2774\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 = 15.1194, size = 58, normalized size = 0.88 \begin{align*} - \frac{45 \left (1 - 2 x\right )^{\frac{5}{2}}}{16} + \frac{85 \left (1 - 2 x\right )^{\frac{3}{2}}}{2} - \frac{3467 \sqrt{1 - 2 x}}{8} - \frac{1309}{2 \sqrt{1 - 2 x}} + \frac{5929}{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 = 2.45791, size = 76, normalized size = 1.15 \begin{align*} -\frac{45}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{85}{2} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3467}{8} \, \sqrt{-2 \, x + 1} - \frac{77 \,{\left (816 \, x - 331\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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