Optimal. Leaf size=66 \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0128068, 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} \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{3773}{16 (1-2 x)^{5/2}}-\frac{3283}{8 (1-2 x)^{3/2}}+\frac{1071}{4 \sqrt{1-2 x}}-\frac{621}{8} \sqrt{1-2 x}+\frac{135}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac{3773}{48 (1-2 x)^{3/2}}-\frac{3283}{8 \sqrt{1-2 x}}-\frac{1071}{4} \sqrt{1-2 x}+\frac{207}{8} (1-2 x)^{3/2}-\frac{27}{16} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0139399, size = 33, normalized size = 0.5 \[ -\frac{81 x^4+459 x^3+2403 x^2-5250 x+1726}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{81\,{x}^{4}+459\,{x}^{3}+2403\,{x}^{2}-5250\,x+1726}{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 = 1.09315, size = 57, normalized size = 0.86 \begin{align*} -\frac{27}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} + \frac{49 \,{\left (804 \, x - 325\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 = 1.55004, size = 115, normalized size = 1.74 \begin{align*} -\frac{{\left (81 \, x^{4} + 459 \, x^{3} + 2403 \, x^{2} - 5250 \, x + 1726\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 = 15.0776, size = 58, normalized size = 0.88 \begin{align*} - \frac{27 \left (1 - 2 x\right )^{\frac{5}{2}}}{16} + \frac{207 \left (1 - 2 x\right )^{\frac{3}{2}}}{8} - \frac{1071 \sqrt{1 - 2 x}}{4} - \frac{3283}{8 \sqrt{1 - 2 x}} + \frac{3773}{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 = 1.70701, size = 76, normalized size = 1.15 \begin{align*} -\frac{27}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} - \frac{49 \,{\left (804 \, x - 325\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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