Optimal. Leaf size=66 \[ -\frac{135}{208} (1-2 x)^{13/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{3773}{80} (1-2 x)^{5/2} \]
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Rubi [A] time = 0.0117495, 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} \[ -\frac{135}{208} (1-2 x)^{13/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{3773}{80} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x) \, dx &=\int \left (\frac{3773}{16} (1-2 x)^{3/2}-\frac{3283}{8} (1-2 x)^{5/2}+\frac{1071}{4} (1-2 x)^{7/2}-\frac{621}{8} (1-2 x)^{9/2}+\frac{135}{16} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{3773}{80} (1-2 x)^{5/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{135}{208} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0145102, size = 33, normalized size = 0.5 \[ -\frac{1}{715} (1-2 x)^{5/2} \left (7425 x^4+25515 x^3+35675 x^2+25310 x+8494\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{7425\,{x}^{4}+25515\,{x}^{3}+35675\,{x}^{2}+25310\,x+8494}{715} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03364, size = 62, normalized size = 0.94 \begin{align*} -\frac{135}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{621}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{119}{4} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{469}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3773}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41249, size = 134, normalized size = 2.03 \begin{align*} -\frac{1}{715} \,{\left (29700 \, x^{6} + 72360 \, x^{5} + 48065 \, x^{4} - 15945 \, x^{3} - 31589 \, x^{2} - 8666 \, x + 8494\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 10.0589, size = 58, normalized size = 0.88 \begin{align*} - \frac{135 \left (1 - 2 x\right )^{\frac{13}{2}}}{208} + \frac{621 \left (1 - 2 x\right )^{\frac{11}{2}}}{88} - \frac{119 \left (1 - 2 x\right )^{\frac{9}{2}}}{4} + \frac{469 \left (1 - 2 x\right )^{\frac{7}{2}}}{8} - \frac{3773 \left (1 - 2 x\right )^{\frac{5}{2}}}{80} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.72545, size = 109, normalized size = 1.65 \begin{align*} -\frac{135}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{621}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{119}{4} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{469}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3773}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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