Optimal. Leaf size=26 \[ 20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x \]
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Rubi [A] time = 0.010321, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ 20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^2 (3+5 x)^2 \, dx &=\int \left (9-6 x-59 x^2+20 x^3+100 x^4\right ) \, dx\\ &=9 x-3 x^2-\frac{59 x^3}{3}+5 x^4+20 x^5\\ \end{align*}
Mathematica [A] time = 0.0008701, size = 26, normalized size = 1. \[ 20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 1. \begin{align*} 9\,x-3\,{x}^{2}-{\frac{59\,{x}^{3}}{3}}+5\,{x}^{4}+20\,{x}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01603, size = 32, normalized size = 1.23 \begin{align*} 20 \, x^{5} + 5 \, x^{4} - \frac{59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32983, size = 55, normalized size = 2.12 \begin{align*} 20 x^{5} + 5 x^{4} - \frac{59}{3} x^{3} - 3 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.056926, size = 24, normalized size = 0.92 \begin{align*} 20 x^{5} + 5 x^{4} - \frac{59 x^{3}}{3} - 3 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.4032, size = 32, normalized size = 1.23 \begin{align*} 20 \, x^{5} + 5 \, x^{4} - \frac{59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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