Optimal. Leaf size=25 \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]
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Rubi [A] time = 0.0100393, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {77} \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x) (3+5 x) \, dx &=\int \left (6+7 x-23 x^2-30 x^3\right ) \, dx\\ &=6 x+\frac{7 x^2}{2}-\frac{23 x^3}{3}-\frac{15 x^4}{2}\\ \end{align*}
Mathematica [A] time = 0.0011068, size = 25, normalized size = 1. \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.8 \begin{align*} 6\,x+{\frac{7\,{x}^{2}}{2}}-{\frac{23\,{x}^{3}}{3}}-{\frac{15\,{x}^{4}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15471, size = 26, normalized size = 1.04 \begin{align*} -\frac{15}{2} \, x^{4} - \frac{23}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30139, size = 51, normalized size = 2.04 \begin{align*} -\frac{15}{2} x^{4} - \frac{23}{3} x^{3} + \frac{7}{2} x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05262, size = 22, normalized size = 0.88 \begin{align*} - \frac{15 x^{4}}{2} - \frac{23 x^{3}}{3} + \frac{7 x^{2}}{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.32116, size = 26, normalized size = 1.04 \begin{align*} -\frac{15}{2} \, x^{4} - \frac{23}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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