Optimal. Leaf size=30 \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]
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Rubi [A] time = 0.0117571, antiderivative size = 30, 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} \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x) (3+5 x)^2 \, dx &=\int \left (18+51 x-34 x^2-205 x^3-150 x^4\right ) \, dx\\ &=18 x+\frac{51 x^2}{2}-\frac{34 x^3}{3}-\frac{205 x^4}{4}-30 x^5\\ \end{align*}
Mathematica [A] time = 0.0006473, size = 30, normalized size = 1. \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*} 18\,x+{\frac{51\,{x}^{2}}{2}}-{\frac{34\,{x}^{3}}{3}}-{\frac{205\,{x}^{4}}{4}}-30\,{x}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.34398, size = 32, normalized size = 1.07 \begin{align*} -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60422, size = 68, normalized size = 2.27 \begin{align*} -30 x^{5} - \frac{205}{4} x^{4} - \frac{34}{3} x^{3} + \frac{51}{2} x^{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.055748, size = 27, normalized size = 0.9 \begin{align*} - 30 x^{5} - \frac{205 x^{4}}{4} - \frac{34 x^{3}}{3} + \frac{51 x^{2}}{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.30499, size = 32, normalized size = 1.07 \begin{align*} -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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