Optimal. Leaf size=42 \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]
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Rubi [A] time = 0.0156931, antiderivative size = 42, 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} \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx &=\int \left (24+52 x-154 x^2-425 x^3+99 x^4+864 x^5+540 x^6\right ) \, dx\\ &=24 x+26 x^2-\frac{154 x^3}{3}-\frac{425 x^4}{4}+\frac{99 x^5}{5}+144 x^6+\frac{540 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.000846, size = 42, normalized size = 1. \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 35, normalized size = 0.8 \begin{align*} 24\,x+26\,{x}^{2}-{\frac{154\,{x}^{3}}{3}}-{\frac{425\,{x}^{4}}{4}}+{\frac{99\,{x}^{5}}{5}}+144\,{x}^{6}+{\frac{540\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04608, size = 46, normalized size = 1.1 \begin{align*} \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.3733, size = 97, normalized size = 2.31 \begin{align*} \frac{540}{7} x^{7} + 144 x^{6} + \frac{99}{5} x^{5} - \frac{425}{4} x^{4} - \frac{154}{3} x^{3} + 26 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061785, size = 39, normalized size = 0.93 \begin{align*} \frac{540 x^{7}}{7} + 144 x^{6} + \frac{99 x^{5}}{5} - \frac{425 x^{4}}{4} - \frac{154 x^{3}}{3} + 26 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.22988, size = 46, normalized size = 1.1 \begin{align*} \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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