Optimal. Leaf size=28 \[ 12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x \]
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Rubi [A] time = 0.0116863, 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} \[ 12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx &=\int \left (6-5 x-37 x^2+16 x^3+60 x^4\right ) \, dx\\ &=6 x-\frac{5 x^2}{2}-\frac{37 x^3}{3}+4 x^4+12 x^5\\ \end{align*}
Mathematica [A] time = 0.0007788, size = 28, normalized size = 1. \[ 12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.9 \begin{align*} 6\,x-{\frac{5\,{x}^{2}}{2}}-{\frac{37\,{x}^{3}}{3}}+4\,{x}^{4}+12\,{x}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04667, size = 32, normalized size = 1.14 \begin{align*} 12 \, x^{5} + 4 \, x^{4} - \frac{37}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30142, size = 58, normalized size = 2.07 \begin{align*} 12 x^{5} + 4 x^{4} - \frac{37}{3} x^{3} - \frac{5}{2} x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060052, size = 26, normalized size = 0.93 \begin{align*} 12 x^{5} + 4 x^{4} - \frac{37 x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.03151, size = 32, normalized size = 1.14 \begin{align*} 12 \, x^{5} + 4 \, x^{4} - \frac{37}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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