Optimal. Leaf size=78 \[ -\frac{1000 (3 x+2)^{13}}{28431}+\frac{925 (3 x+2)^{12}}{2187}-\frac{14390 (3 x+2)^{11}}{8019}+\frac{66193 (3 x+2)^{10}}{21870}-\frac{10073 (3 x+2)^9}{6561}+\frac{1813 (3 x+2)^8}{5832}-\frac{49 (3 x+2)^7}{2187} \]
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Rubi [A] time = 0.0345636, antiderivative size = 78, 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 = {88} \[ -\frac{1000 (3 x+2)^{13}}{28431}+\frac{925 (3 x+2)^{12}}{2187}-\frac{14390 (3 x+2)^{11}}{8019}+\frac{66193 (3 x+2)^{10}}{21870}-\frac{10073 (3 x+2)^9}{6561}+\frac{1813 (3 x+2)^8}{5832}-\frac{49 (3 x+2)^7}{2187} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx &=\int \left (-\frac{343}{729} (2+3 x)^6+\frac{1813}{243} (2+3 x)^7-\frac{10073}{243} (2+3 x)^8+\frac{66193}{729} (2+3 x)^9-\frac{14390}{243} (2+3 x)^{10}+\frac{3700}{243} (2+3 x)^{11}-\frac{1000}{729} (2+3 x)^{12}\right ) \, dx\\ &=-\frac{49 (2+3 x)^7}{2187}+\frac{1813 (2+3 x)^8}{5832}-\frac{10073 (2+3 x)^9}{6561}+\frac{66193 (2+3 x)^{10}}{21870}-\frac{14390 (2+3 x)^{11}}{8019}+\frac{925 (2+3 x)^{12}}{2187}-\frac{1000 (2+3 x)^{13}}{28431}\\ \end{align*}
Mathematica [A] time = 0.0026811, size = 74, normalized size = 0.95 \[ -\frac{729000 x^{13}}{13}-261225 x^{12}-\frac{5100570 x^{11}}{11}-\frac{3110589 x^{10}}{10}+122655 x^9+\frac{2623581 x^8}{8}+155453 x^7-51908 x^6-\frac{390396 x^5}{5}-20140 x^4+8688 x^3+6912 x^2+1728 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 65, normalized size = 0.8 \begin{align*} -{\frac{729000\,{x}^{13}}{13}}-261225\,{x}^{12}-{\frac{5100570\,{x}^{11}}{11}}-{\frac{3110589\,{x}^{10}}{10}}+122655\,{x}^{9}+{\frac{2623581\,{x}^{8}}{8}}+155453\,{x}^{7}-51908\,{x}^{6}-{\frac{390396\,{x}^{5}}{5}}-20140\,{x}^{4}+8688\,{x}^{3}+6912\,{x}^{2}+1728\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.90446, size = 86, normalized size = 1.1 \begin{align*} -\frac{729000}{13} \, x^{13} - 261225 \, x^{12} - \frac{5100570}{11} \, x^{11} - \frac{3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac{2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac{390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.16562, size = 242, normalized size = 3.1 \begin{align*} -\frac{729000}{13} x^{13} - 261225 x^{12} - \frac{5100570}{11} x^{11} - \frac{3110589}{10} x^{10} + 122655 x^{9} + \frac{2623581}{8} x^{8} + 155453 x^{7} - 51908 x^{6} - \frac{390396}{5} x^{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074929, size = 71, normalized size = 0.91 \begin{align*} - \frac{729000 x^{13}}{13} - 261225 x^{12} - \frac{5100570 x^{11}}{11} - \frac{3110589 x^{10}}{10} + 122655 x^{9} + \frac{2623581 x^{8}}{8} + 155453 x^{7} - 51908 x^{6} - \frac{390396 x^{5}}{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.74099, size = 86, normalized size = 1.1 \begin{align*} -\frac{729000}{13} \, x^{13} - 261225 \, x^{12} - \frac{5100570}{11} \, x^{11} - \frac{3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac{2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac{390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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