Optimal. Leaf size=28 \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]
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Rubi [A] time = 0.012096, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]
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) \, dx &=\int \left (12+32 x-25 x^2-129 x^3-90 x^4\right ) \, dx\\ &=12 x+16 x^2-\frac{25 x^3}{3}-\frac{129 x^4}{4}-18 x^5\\ \end{align*}
Mathematica [A] time = 0.0008591, size = 28, normalized size = 1. \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.9 \begin{align*} 12\,x+16\,{x}^{2}-{\frac{25\,{x}^{3}}{3}}-{\frac{129\,{x}^{4}}{4}}-18\,{x}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.2363, size = 32, normalized size = 1.14 \begin{align*} -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27884, size = 65, normalized size = 2.32 \begin{align*} -18 x^{5} - \frac{129}{4} x^{4} - \frac{25}{3} x^{3} + 16 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.055785, size = 26, normalized size = 0.93 \begin{align*} - 18 x^{5} - \frac{129 x^{4}}{4} - \frac{25 x^{3}}{3} + 16 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.77552, size = 32, normalized size = 1.14 \begin{align*} -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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