Optimal. Leaf size=56 \[ -\frac{40 (3 x+2)^9}{2187}+\frac{107}{486} (3 x+2)^8-\frac{74}{81} (3 x+2)^7+\frac{2009 (3 x+2)^6}{1458}-\frac{343 (3 x+2)^5}{1215} \]
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Rubi [A] time = 0.0225159, antiderivative size = 56, 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} \[ -\frac{40 (3 x+2)^9}{2187}+\frac{107}{486} (3 x+2)^8-\frac{74}{81} (3 x+2)^7+\frac{2009 (3 x+2)^6}{1458}-\frac{343 (3 x+2)^5}{1215} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^4+\frac{2009}{81} (2+3 x)^5-\frac{518}{27} (2+3 x)^6+\frac{428}{81} (2+3 x)^7-\frac{40}{81} (2+3 x)^8\right ) \, dx\\ &=-\frac{343 (2+3 x)^5}{1215}+\frac{2009 (2+3 x)^6}{1458}-\frac{74}{81} (2+3 x)^7+\frac{107}{486} (2+3 x)^8-\frac{40 (2+3 x)^9}{2187}\\ \end{align*}
Mathematica [A] time = 0.001982, size = 50, normalized size = 0.89 \[ -360 x^9-\frac{1431 x^8}{2}-54 x^7+\frac{1393 x^6}{2}+\frac{1547 x^5}{5}-252 x^4-168 x^3+40 x^2+48 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 0.8 \begin{align*} -360\,{x}^{9}-{\frac{1431\,{x}^{8}}{2}}-54\,{x}^{7}+{\frac{1393\,{x}^{6}}{2}}+{\frac{1547\,{x}^{5}}{5}}-252\,{x}^{4}-168\,{x}^{3}+40\,{x}^{2}+48\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.20624, size = 59, normalized size = 1.05 \begin{align*} -360 \, x^{9} - \frac{1431}{2} \, x^{8} - 54 \, x^{7} + \frac{1393}{2} \, x^{6} + \frac{1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.07901, size = 127, normalized size = 2.27 \begin{align*} -360 x^{9} - \frac{1431}{2} x^{8} - 54 x^{7} + \frac{1393}{2} x^{6} + \frac{1547}{5} x^{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.064435, size = 48, normalized size = 0.86 \begin{align*} - 360 x^{9} - \frac{1431 x^{8}}{2} - 54 x^{7} + \frac{1393 x^{6}}{2} + \frac{1547 x^{5}}{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.07132, size = 59, normalized size = 1.05 \begin{align*} -360 \, x^{9} - \frac{1431}{2} \, x^{8} - 54 \, x^{7} + \frac{1393}{2} \, x^{6} + \frac{1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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