Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]
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Rubi [A] time = 0.0320184, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx &=\int \left (-\frac{7}{81} (2+3 x)^8+\frac{107}{81} (2+3 x)^9-\frac{185}{27} (2+3 x)^{10}+\frac{1025}{81} (2+3 x)^{11}-\frac{250}{81} (2+3 x)^{12}\right ) \, dx\\ &=-\frac{7 (2+3 x)^9}{2187}+\frac{107 (2+3 x)^{10}}{2430}-\frac{185}{891} (2+3 x)^{11}+\frac{1025 (2+3 x)^{12}}{2916}-\frac{250 (2+3 x)^{13}}{3159}\\ \end{align*}
Mathematica [A] time = 0.0024004, size = 74, normalized size = 1.32 \[ -\frac{1640250 x^{13}}{13}-\frac{3626775 x^{12}}{4}-\frac{32079645 x^{11}}{11}-\frac{54794799 x^{10}}{10}-6524829 x^9-4865076 x^8-1830960 x^7+350128 x^6+\frac{4580384 x^5}{5}+597824 x^4+224256 x^3+51840 x^2+6912 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 65, normalized size = 1.2 \begin{align*} -{\frac{1640250\,{x}^{13}}{13}}-{\frac{3626775\,{x}^{12}}{4}}-{\frac{32079645\,{x}^{11}}{11}}-{\frac{54794799\,{x}^{10}}{10}}-6524829\,{x}^{9}-4865076\,{x}^{8}-1830960\,{x}^{7}+350128\,{x}^{6}+{\frac{4580384\,{x}^{5}}{5}}+597824\,{x}^{4}+224256\,{x}^{3}+51840\,{x}^{2}+6912\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11687, size = 86, normalized size = 1.54 \begin{align*} -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61024, size = 258, normalized size = 4.61 \begin{align*} -\frac{1640250}{13} x^{13} - \frac{3626775}{4} x^{12} - \frac{32079645}{11} x^{11} - \frac{54794799}{10} x^{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384}{5} x^{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.075412, size = 71, normalized size = 1.27 \begin{align*} - \frac{1640250 x^{13}}{13} - \frac{3626775 x^{12}}{4} - \frac{32079645 x^{11}}{11} - \frac{54794799 x^{10}}{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384 x^{5}}{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.18005, size = 86, normalized size = 1.54 \begin{align*} -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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