Optimal. Leaf size=46 \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]
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Rubi [A] time = 0.01598, antiderivative size = 46, 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} \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx &=\int \left (18-21 x-166 x^2+135 x^3+534 x^4-220 x^5-600 x^6\right ) \, dx\\ &=18 x-\frac{21 x^2}{2}-\frac{166 x^3}{3}+\frac{135 x^4}{4}+\frac{534 x^5}{5}-\frac{110 x^6}{3}-\frac{600 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0008486, size = 46, normalized size = 1. \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 18\,x-{\frac{21\,{x}^{2}}{2}}-{\frac{166\,{x}^{3}}{3}}+{\frac{135\,{x}^{4}}{4}}+{\frac{534\,{x}^{5}}{5}}-{\frac{110\,{x}^{6}}{3}}-{\frac{600\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02157, size = 46, normalized size = 1. \begin{align*} -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.14342, size = 105, normalized size = 2.28 \begin{align*} -\frac{600}{7} x^{7} - \frac{110}{3} x^{6} + \frac{534}{5} x^{5} + \frac{135}{4} x^{4} - \frac{166}{3} x^{3} - \frac{21}{2} x^{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060589, size = 42, normalized size = 0.91 \begin{align*} - \frac{600 x^{7}}{7} - \frac{110 x^{6}}{3} + \frac{534 x^{5}}{5} + \frac{135 x^{4}}{4} - \frac{166 x^{3}}{3} - \frac{21 x^{2}}{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.63564, size = 46, normalized size = 1. \begin{align*} -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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