Optimal. Leaf size=59 \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]
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Rubi [A] time = 0.0249694, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+756 x-1602 x^2-8693 x^3-1419 x^4+31539 x^5+33013 x^6-28710 x^7-62100 x^8-27000 x^9\right ) \, dx\\ &=216 x+378 x^2-534 x^3-\frac{8693 x^4}{4}-\frac{1419 x^5}{5}+\frac{10513 x^6}{2}+\frac{33013 x^7}{7}-\frac{14355 x^8}{4}-6900 x^9-2700 x^{10}\\ \end{align*}
Mathematica [A] time = 0.0024707, size = 59, normalized size = 1. \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 50, normalized size = 0.9 \begin{align*} 216\,x+378\,{x}^{2}-534\,{x}^{3}-{\frac{8693\,{x}^{4}}{4}}-{\frac{1419\,{x}^{5}}{5}}+{\frac{10513\,{x}^{6}}{2}}+{\frac{33013\,{x}^{7}}{7}}-{\frac{14355\,{x}^{8}}{4}}-6900\,{x}^{9}-2700\,{x}^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04065, size = 66, normalized size = 1.12 \begin{align*} -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.03422, size = 161, normalized size = 2.73 \begin{align*} -2700 x^{10} - 6900 x^{9} - \frac{14355}{4} x^{8} + \frac{33013}{7} x^{7} + \frac{10513}{2} x^{6} - \frac{1419}{5} x^{5} - \frac{8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066971, size = 56, normalized size = 0.95 \begin{align*} - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.55003, size = 66, normalized size = 1.12 \begin{align*} -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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