Optimal. Leaf size=66 \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.013909, 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} \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]
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)^{3/2}} \, dx &=\int \left (\frac{5929}{16 (1-2 x)^{3/2}}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{3467}{8} \sqrt{1-2 x}-\frac{255}{2} (1-2 x)^{3/2}+\frac{225}{16} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac{5929}{16 \sqrt{1-2 x}}+\frac{1309}{2} \sqrt{1-2 x}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{225}{112} (1-2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0131212, size = 33, normalized size = 0.5 \[ \frac{-675 x^4-2934 x^3-6721 x^2-18230 x+18986}{21 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 30, normalized size = 0.5 \begin{align*} -{\frac{675\,{x}^{4}+2934\,{x}^{3}+6721\,{x}^{2}+18230\,x-18986}{21}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.19176, size = 62, normalized size = 0.94 \begin{align*} -\frac{225}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{51}{2} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52847, size = 109, normalized size = 1.65 \begin{align*} \frac{{\left (675 \, x^{4} + 2934 \, x^{3} + 6721 \, x^{2} + 18230 \, x - 18986\right )} \sqrt{-2 \, x + 1}}{21 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 16.4108, size = 58, normalized size = 0.88 \begin{align*} - \frac{225 \left (1 - 2 x\right )^{\frac{7}{2}}}{112} + \frac{51 \left (1 - 2 x\right )^{\frac{5}{2}}}{2} - \frac{3467 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} + \frac{1309 \sqrt{1 - 2 x}}{2} + \frac{5929}{16 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.96152, size = 81, normalized size = 1.23 \begin{align*} \frac{225}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{51}{2} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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