Optimal. Leaf size=66 \[ -\frac{9}{16} (1-2 x)^{15/2}+\frac{621}{104} (1-2 x)^{13/2}-\frac{1071}{44} (1-2 x)^{11/2}+\frac{3283}{72} (1-2 x)^{9/2}-\frac{539}{16} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.0124508, 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} \[ -\frac{9}{16} (1-2 x)^{15/2}+\frac{621}{104} (1-2 x)^{13/2}-\frac{1071}{44} (1-2 x)^{11/2}+\frac{3283}{72} (1-2 x)^{9/2}-\frac{539}{16} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x) \, dx &=\int \left (\frac{3773}{16} (1-2 x)^{5/2}-\frac{3283}{8} (1-2 x)^{7/2}+\frac{1071}{4} (1-2 x)^{9/2}-\frac{621}{8} (1-2 x)^{11/2}+\frac{135}{16} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{539}{16} (1-2 x)^{7/2}+\frac{3283}{72} (1-2 x)^{9/2}-\frac{1071}{44} (1-2 x)^{11/2}+\frac{621}{104} (1-2 x)^{13/2}-\frac{9}{16} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0170494, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{7/2} \left (11583 x^4+38313 x^3+50463 x^2+32378 x+9038\right )}{1287} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 30, normalized size = 0.5 \begin{align*} -{\frac{11583\,{x}^{4}+38313\,{x}^{3}+50463\,{x}^{2}+32378\,x+9038}{1287} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.82798, size = 62, normalized size = 0.94 \begin{align*} -\frac{9}{16} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{621}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{1071}{44} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{3283}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{539}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48099, size = 154, normalized size = 2.33 \begin{align*} \frac{1}{1287} \,{\left (92664 \, x^{7} + 167508 \, x^{6} + 13446 \, x^{5} - 128237 \, x^{4} - 51767 \, x^{3} + 35349 \, x^{2} + 21850 \, x - 9038\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 13.895, size = 58, normalized size = 0.88 \begin{align*} - \frac{9 \left (1 - 2 x\right )^{\frac{15}{2}}}{16} + \frac{621 \left (1 - 2 x\right )^{\frac{13}{2}}}{104} - \frac{1071 \left (1 - 2 x\right )^{\frac{11}{2}}}{44} + \frac{3283 \left (1 - 2 x\right )^{\frac{9}{2}}}{72} - \frac{539 \left (1 - 2 x\right )^{\frac{7}{2}}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.59962, size = 109, normalized size = 1.65 \begin{align*} \frac{9}{16} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{621}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{1071}{44} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{3283}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{539}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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