Optimal. Leaf size=23 \[ -\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x \]
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Rubi [A] time = 0.0087208, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ -\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x) (3+5 x)^2 \, dx &=\int \left (9+12 x-35 x^2-50 x^3\right ) \, dx\\ &=9 x+6 x^2-\frac{35 x^3}{3}-\frac{25 x^4}{2}\\ \end{align*}
Mathematica [A] time = 0.0005931, size = 23, normalized size = 1. \[ -\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 20, normalized size = 0.9 \begin{align*} 9\,x+6\,{x}^{2}-{\frac{35\,{x}^{3}}{3}}-{\frac{25\,{x}^{4}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28646, size = 26, normalized size = 1.13 \begin{align*} -\frac{25}{2} \, x^{4} - \frac{35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57788, size = 49, normalized size = 2.13 \begin{align*} -\frac{25}{2} x^{4} - \frac{35}{3} x^{3} + 6 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.056882, size = 20, normalized size = 0.87 \begin{align*} - \frac{25 x^{4}}{2} - \frac{35 x^{3}}{3} + 6 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.23608, size = 26, normalized size = 1.13 \begin{align*} -\frac{25}{2} \, x^{4} - \frac{35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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