Optimal. Leaf size=35 \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]
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Rubi [A] time = 0.0138977, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]
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)^2 \, dx &=\int \left (18+15 x-136 x^2-137 x^3+260 x^4+300 x^5\right ) \, dx\\ &=18 x+\frac{15 x^2}{2}-\frac{136 x^3}{3}-\frac{137 x^4}{4}+52 x^5+50 x^6\\ \end{align*}
Mathematica [A] time = 0.0007696, size = 35, normalized size = 1. \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 30, normalized size = 0.9 \begin{align*} 18\,x+{\frac{15\,{x}^{2}}{2}}-{\frac{136\,{x}^{3}}{3}}-{\frac{137\,{x}^{4}}{4}}+52\,{x}^{5}+50\,{x}^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.38883, size = 39, normalized size = 1.11 \begin{align*} 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28191, size = 80, normalized size = 2.29 \begin{align*} 50 x^{6} + 52 x^{5} - \frac{137}{4} x^{4} - \frac{136}{3} x^{3} + \frac{15}{2} x^{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058923, size = 32, normalized size = 0.91 \begin{align*} 50 x^{6} + 52 x^{5} - \frac{137 x^{4}}{4} - \frac{136 x^{3}}{3} + \frac{15 x^{2}}{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.03849, size = 39, normalized size = 1.11 \begin{align*} 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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