Optimal. Leaf size=34 \[ -\frac{10}{189} (3 x+2)^7+\frac{37}{162} (3 x+2)^6-\frac{7}{135} (3 x+2)^5 \]
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Rubi [A] time = 0.0165138, antiderivative size = 34, 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} \[ -\frac{10}{189} (3 x+2)^7+\frac{37}{162} (3 x+2)^6-\frac{7}{135} (3 x+2)^5 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^4 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^4+\frac{37}{9} (2+3 x)^5-\frac{10}{9} (2+3 x)^6\right ) \, dx\\ &=-\frac{7}{135} (2+3 x)^5+\frac{37}{162} (2+3 x)^6-\frac{10}{189} (2+3 x)^7\\ \end{align*}
Mathematica [A] time = 0.0010793, size = 42, normalized size = 1.24 \[ -\frac{810 x^7}{7}-\frac{747 x^6}{2}-\frac{2133 x^5}{5}-132 x^4+\frac{392 x^3}{3}+136 x^2+48 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 35, normalized size = 1. \begin{align*} -{\frac{810\,{x}^{7}}{7}}-{\frac{747\,{x}^{6}}{2}}-{\frac{2133\,{x}^{5}}{5}}-132\,{x}^{4}+{\frac{392\,{x}^{3}}{3}}+136\,{x}^{2}+48\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.74737, size = 46, normalized size = 1.35 \begin{align*} -\frac{810}{7} \, x^{7} - \frac{747}{2} \, x^{6} - \frac{2133}{5} \, x^{5} - 132 \, x^{4} + \frac{392}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29736, size = 103, normalized size = 3.03 \begin{align*} -\frac{810}{7} x^{7} - \frac{747}{2} x^{6} - \frac{2133}{5} x^{5} - 132 x^{4} + \frac{392}{3} x^{3} + 136 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060902, size = 39, normalized size = 1.15 \begin{align*} - \frac{810 x^{7}}{7} - \frac{747 x^{6}}{2} - \frac{2133 x^{5}}{5} - 132 x^{4} + \frac{392 x^{3}}{3} + 136 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.98187, size = 46, normalized size = 1.35 \begin{align*} -\frac{810}{7} \, x^{7} - \frac{747}{2} \, x^{6} - \frac{2133}{5} \, x^{5} - 132 \, x^{4} + \frac{392}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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