Optimal. Leaf size=96 \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]
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Rubi [A] time = 0.0705267, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {1657} \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^4 \, dx &=\int \left (432+2160 x+8568 x^2+20576 x^3+43083 x^4+64529 x^5+91349 x^6+94881 x^7+103583 x^8+75311 x^9+68583 x^{10}+30395 x^{11}+27050 x^{12}+4500 x^{13}+5000 x^{14}\right ) \, dx\\ &=432 x+1080 x^2+2856 x^3+5144 x^4+\frac{43083 x^5}{5}+\frac{64529 x^6}{6}+\frac{91349 x^7}{7}+\frac{94881 x^8}{8}+\frac{103583 x^9}{9}+\frac{75311 x^{10}}{10}+\frac{68583 x^{11}}{11}+\frac{30395 x^{12}}{12}+\frac{27050 x^{13}}{13}+\frac{2250 x^{14}}{7}+\frac{1000 x^{15}}{3}\\ \end{align*}
Mathematica [A] time = 0.0029899, size = 96, normalized size = 1. \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 75, normalized size = 0.8 \begin{align*} 432\,x+1080\,{x}^{2}+2856\,{x}^{3}+5144\,{x}^{4}+{\frac{43083\,{x}^{5}}{5}}+{\frac{64529\,{x}^{6}}{6}}+{\frac{91349\,{x}^{7}}{7}}+{\frac{94881\,{x}^{8}}{8}}+{\frac{103583\,{x}^{9}}{9}}+{\frac{75311\,{x}^{10}}{10}}+{\frac{68583\,{x}^{11}}{11}}+{\frac{30395\,{x}^{12}}{12}}+{\frac{27050\,{x}^{13}}{13}}+{\frac{2250\,{x}^{14}}{7}}+{\frac{1000\,{x}^{15}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983455, size = 100, normalized size = 1.04 \begin{align*} \frac{1000}{3} \, x^{15} + \frac{2250}{7} \, x^{14} + \frac{27050}{13} \, x^{13} + \frac{30395}{12} \, x^{12} + \frac{68583}{11} \, x^{11} + \frac{75311}{10} \, x^{10} + \frac{103583}{9} \, x^{9} + \frac{94881}{8} \, x^{8} + \frac{91349}{7} \, x^{7} + \frac{64529}{6} \, x^{6} + \frac{43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.823481, size = 274, normalized size = 2.85 \begin{align*} \frac{1000}{3} x^{15} + \frac{2250}{7} x^{14} + \frac{27050}{13} x^{13} + \frac{30395}{12} x^{12} + \frac{68583}{11} x^{11} + \frac{75311}{10} x^{10} + \frac{103583}{9} x^{9} + \frac{94881}{8} x^{8} + \frac{91349}{7} x^{7} + \frac{64529}{6} x^{6} + \frac{43083}{5} x^{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.126187, size = 92, normalized size = 0.96 \begin{align*} \frac{1000 x^{15}}{3} + \frac{2250 x^{14}}{7} + \frac{27050 x^{13}}{13} + \frac{30395 x^{12}}{12} + \frac{68583 x^{11}}{11} + \frac{75311 x^{10}}{10} + \frac{103583 x^{9}}{9} + \frac{94881 x^{8}}{8} + \frac{91349 x^{7}}{7} + \frac{64529 x^{6}}{6} + \frac{43083 x^{5}}{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17693, size = 100, normalized size = 1.04 \begin{align*} \frac{1000}{3} \, x^{15} + \frac{2250}{7} \, x^{14} + \frac{27050}{13} \, x^{13} + \frac{30395}{12} \, x^{12} + \frac{68583}{11} \, x^{11} + \frac{75311}{10} \, x^{10} + \frac{103583}{9} \, x^{9} + \frac{94881}{8} \, x^{8} + \frac{91349}{7} \, x^{7} + \frac{64529}{6} \, x^{6} + \frac{43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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