Optimal. Leaf size=49 \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]
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Rubi [A] time = 0.0196127, antiderivative size = 49, 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} \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (108+432 x-261 x^2-3181 x^3-3083 x^4+4685 x^5+9600 x^6+4500 x^7\right ) \, dx\\ &=108 x+216 x^2-87 x^3-\frac{3181 x^4}{4}-\frac{3083 x^5}{5}+\frac{4685 x^6}{6}+\frac{9600 x^7}{7}+\frac{1125 x^8}{2}\\ \end{align*}
Mathematica [A] time = 0.0023153, size = 49, normalized size = 1. \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 40, normalized size = 0.8 \begin{align*} 108\,x+216\,{x}^{2}-87\,{x}^{3}-{\frac{3181\,{x}^{4}}{4}}-{\frac{3083\,{x}^{5}}{5}}+{\frac{4685\,{x}^{6}}{6}}+{\frac{9600\,{x}^{7}}{7}}+{\frac{1125\,{x}^{8}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16172, size = 53, normalized size = 1.08 \begin{align*} \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54467, size = 123, normalized size = 2.51 \begin{align*} \frac{1125}{2} x^{8} + \frac{9600}{7} x^{7} + \frac{4685}{6} x^{6} - \frac{3083}{5} x^{5} - \frac{3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063659, size = 46, normalized size = 0.94 \begin{align*} \frac{1125 x^{8}}{2} + \frac{9600 x^{7}}{7} + \frac{4685 x^{6}}{6} - \frac{3083 x^{5}}{5} - \frac{3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.41522, size = 53, normalized size = 1.08 \begin{align*} \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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