Optimal. Leaf size=31 \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]
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Rubi [A] time = 0.014905, antiderivative size = 31, 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} \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+156 x+85 x^2-512 x^3-915 x^4-450 x^5\right ) \, dx\\ &=36 x+78 x^2+\frac{85 x^3}{3}-128 x^4-183 x^5-75 x^6\\ \end{align*}
Mathematica [A] time = 0.0009216, size = 31, normalized size = 1. \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 1. \begin{align*} 36\,x+78\,{x}^{2}+{\frac{85\,{x}^{3}}{3}}-128\,{x}^{4}-183\,{x}^{5}-75\,{x}^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10817, size = 39, normalized size = 1.26 \begin{align*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45327, size = 76, normalized size = 2.45 \begin{align*} -75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85}{3} x^{3} + 78 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058688, size = 29, normalized size = 0.94 \begin{align*} - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85 x^{3}}{3} + 78 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.61112, size = 39, normalized size = 1.26 \begin{align*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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