Optimal. Leaf size=49 \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]
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Rubi [A] time = 0.0192387, antiderivative size = 49, 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} \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+1620 x+4014 x^2+883 x^3-13943 x^4-27765 x^5-22275 x^6-6750 x^7\right ) \, dx\\ &=216 x+810 x^2+1338 x^3+\frac{883 x^4}{4}-\frac{13943 x^5}{5}-\frac{9255 x^6}{2}-\frac{22275 x^7}{7}-\frac{3375 x^8}{4}\\ \end{align*}
Mathematica [A] time = 0.0009678, size = 49, normalized size = 1. \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 40, normalized size = 0.8 \begin{align*} 216\,x+810\,{x}^{2}+1338\,{x}^{3}+{\frac{883\,{x}^{4}}{4}}-{\frac{13943\,{x}^{5}}{5}}-{\frac{9255\,{x}^{6}}{2}}-{\frac{22275\,{x}^{7}}{7}}-{\frac{3375\,{x}^{8}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07152, size = 53, normalized size = 1.08 \begin{align*} -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59017, size = 128, normalized size = 2.61 \begin{align*} -\frac{3375}{4} x^{8} - \frac{22275}{7} x^{7} - \frac{9255}{2} x^{6} - \frac{13943}{5} x^{5} + \frac{883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.064308, size = 46, normalized size = 0.94 \begin{align*} - \frac{3375 x^{8}}{4} - \frac{22275 x^{7}}{7} - \frac{9255 x^{6}}{2} - \frac{13943 x^{5}}{5} + \frac{883 x^{4}}{4} + 1338 x^{3} + 810 x^{2} + 216 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.83056, size = 53, normalized size = 1.08 \begin{align*} -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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