Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]
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Rubi [A] time = 0.0324613, antiderivative size = 67, 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} \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^7+\frac{763}{243} (2+3 x)^8-\frac{4099}{243} (2+3 x)^9+\frac{8285}{243} (2+3 x)^{10}-\frac{3800}{243} (2+3 x)^{11}+\frac{500}{243} (2+3 x)^{12}\right ) \, dx\\ &=-\frac{49 (2+3 x)^8}{5832}+\frac{763 (2+3 x)^9}{6561}-\frac{4099 (2+3 x)^{10}}{7290}+\frac{8285 (2+3 x)^{11}}{8019}-\frac{950 (2+3 x)^{12}}{2187}+\frac{500 (2+3 x)^{13}}{9477}\\ \end{align*}
Mathematica [A] time = 0.0025098, size = 76, normalized size = 1.13 \[ \frac{1093500 x^{13}}{13}+498150 x^{12}+\frac{13774455 x^{11}}{11}+\frac{16653681 x^{10}}{10}+1086843 x^9-\frac{148473 x^8}{8}-618582 x^7-\frac{1393018 x^6}{3}-\frac{495976 x^5}{5}+65812 x^4+57696 x^3+19872 x^2+3456 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 65, normalized size = 1. \begin{align*}{\frac{1093500\,{x}^{13}}{13}}+498150\,{x}^{12}+{\frac{13774455\,{x}^{11}}{11}}+{\frac{16653681\,{x}^{10}}{10}}+1086843\,{x}^{9}-{\frac{148473\,{x}^{8}}{8}}-618582\,{x}^{7}-{\frac{1393018\,{x}^{6}}{3}}-{\frac{495976\,{x}^{5}}{5}}+65812\,{x}^{4}+57696\,{x}^{3}+19872\,{x}^{2}+3456\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06646, size = 86, normalized size = 1.28 \begin{align*} \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47861, size = 252, normalized size = 3.76 \begin{align*} \frac{1093500}{13} x^{13} + 498150 x^{12} + \frac{13774455}{11} x^{11} + \frac{16653681}{10} x^{10} + 1086843 x^{9} - \frac{148473}{8} x^{8} - 618582 x^{7} - \frac{1393018}{3} x^{6} - \frac{495976}{5} x^{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074877, size = 73, normalized size = 1.09 \begin{align*} \frac{1093500 x^{13}}{13} + 498150 x^{12} + \frac{13774455 x^{11}}{11} + \frac{16653681 x^{10}}{10} + 1086843 x^{9} - \frac{148473 x^{8}}{8} - 618582 x^{7} - \frac{1393018 x^{6}}{3} - \frac{495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.88717, size = 86, normalized size = 1.28 \begin{align*} \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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