Optimal. Leaf size=66 \[ -\frac{135}{112} (1-2 x)^{7/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{357}{4} (1-2 x)^{3/2}+\frac{3283}{8} \sqrt{1-2 x}+\frac{3773}{16 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0119846, 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} \[ -\frac{135}{112} (1-2 x)^{7/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{357}{4} (1-2 x)^{3/2}+\frac{3283}{8} \sqrt{1-2 x}+\frac{3773}{16 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{3773}{16 (1-2 x)^{3/2}}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{1071}{4} \sqrt{1-2 x}-\frac{621}{8} (1-2 x)^{3/2}+\frac{135}{16} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac{3773}{16 \sqrt{1-2 x}}+\frac{3283}{8} \sqrt{1-2 x}-\frac{357}{4} (1-2 x)^{3/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{135}{112} (1-2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0127104, size = 33, normalized size = 0.5 \[ \frac{-675 x^4-2997 x^3-6987 x^2-19154 x+19994}{35 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 30, normalized size = 0.5 \begin{align*} -{\frac{675\,{x}^{4}+2997\,{x}^{3}+6987\,{x}^{2}+19154\,x-19994}{35}{\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 = 3.14171, size = 62, normalized size = 0.94 \begin{align*} -\frac{135}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{621}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{357}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3283}{8} \, \sqrt{-2 \, x + 1} + \frac{3773}{16 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67488, size = 109, normalized size = 1.65 \begin{align*} \frac{{\left (675 \, x^{4} + 2997 \, x^{3} + 6987 \, x^{2} + 19154 \, x - 19994\right )} \sqrt{-2 \, x + 1}}{35 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 16.2832, size = 58, normalized size = 0.88 \begin{align*} - \frac{135 \left (1 - 2 x\right )^{\frac{7}{2}}}{112} + \frac{621 \left (1 - 2 x\right )^{\frac{5}{2}}}{40} - \frac{357 \left (1 - 2 x\right )^{\frac{3}{2}}}{4} + \frac{3283 \sqrt{1 - 2 x}}{8} + \frac{3773}{16 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.23297, size = 81, normalized size = 1.23 \begin{align*} \frac{135}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{621}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{357}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3283}{8} \, \sqrt{-2 \, x + 1} + \frac{3773}{16 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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