Optimal. Leaf size=68 \[ \frac{1250 x^{11}}{11}+\frac{475 x^{10}}{2}+\frac{5075 x^9}{9}+\frac{3415 x^8}{4}+1176 x^7+\frac{2377 x^6}{2}+\frac{5099 x^5}{5}+656 x^4+\frac{1064 x^3}{3}+136 x^2+48 x \]
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Rubi [A] time = 0.0491625, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {1657} \[ \frac{1250 x^{11}}{11}+\frac{475 x^{10}}{2}+\frac{5075 x^9}{9}+\frac{3415 x^8}{4}+1176 x^7+\frac{2377 x^6}{2}+\frac{5099 x^5}{5}+656 x^4+\frac{1064 x^3}{3}+136 x^2+48 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right )^4 \, dx &=\int \left (48+272 x+1064 x^2+2624 x^3+5099 x^4+7131 x^5+8232 x^6+6830 x^7+5075 x^8+2375 x^9+1250 x^{10}\right ) \, dx\\ &=48 x+136 x^2+\frac{1064 x^3}{3}+656 x^4+\frac{5099 x^5}{5}+\frac{2377 x^6}{2}+1176 x^7+\frac{3415 x^8}{4}+\frac{5075 x^9}{9}+\frac{475 x^{10}}{2}+\frac{1250 x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.0026852, size = 68, normalized size = 1. \[ \frac{1250 x^{11}}{11}+\frac{475 x^{10}}{2}+\frac{5075 x^9}{9}+\frac{3415 x^8}{4}+1176 x^7+\frac{2377 x^6}{2}+\frac{5099 x^5}{5}+656 x^4+\frac{1064 x^3}{3}+136 x^2+48 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 55, normalized size = 0.8 \begin{align*} 48\,x+136\,{x}^{2}+{\frac{1064\,{x}^{3}}{3}}+656\,{x}^{4}+{\frac{5099\,{x}^{5}}{5}}+{\frac{2377\,{x}^{6}}{2}}+1176\,{x}^{7}+{\frac{3415\,{x}^{8}}{4}}+{\frac{5075\,{x}^{9}}{9}}+{\frac{475\,{x}^{10}}{2}}+{\frac{1250\,{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.972346, size = 73, normalized size = 1.07 \begin{align*} \frac{1250}{11} \, x^{11} + \frac{475}{2} \, x^{10} + \frac{5075}{9} \, x^{9} + \frac{3415}{4} \, x^{8} + 1176 \, x^{7} + \frac{2377}{2} \, x^{6} + \frac{5099}{5} \, x^{5} + 656 \, x^{4} + \frac{1064}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.847187, size = 176, normalized size = 2.59 \begin{align*} \frac{1250}{11} x^{11} + \frac{475}{2} x^{10} + \frac{5075}{9} x^{9} + \frac{3415}{4} x^{8} + 1176 x^{7} + \frac{2377}{2} x^{6} + \frac{5099}{5} x^{5} + 656 x^{4} + \frac{1064}{3} x^{3} + 136 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.084379, size = 65, normalized size = 0.96 \begin{align*} \frac{1250 x^{11}}{11} + \frac{475 x^{10}}{2} + \frac{5075 x^{9}}{9} + \frac{3415 x^{8}}{4} + 1176 x^{7} + \frac{2377 x^{6}}{2} + \frac{5099 x^{5}}{5} + 656 x^{4} + \frac{1064 x^{3}}{3} + 136 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15386, size = 73, normalized size = 1.07 \begin{align*} \frac{1250}{11} \, x^{11} + \frac{475}{2} \, x^{10} + \frac{5075}{9} \, x^{9} + \frac{3415}{4} \, x^{8} + 1176 \, x^{7} + \frac{2377}{2} \, x^{6} + \frac{5099}{5} \, x^{5} + 656 \, x^{4} + \frac{1064}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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