Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^9}{2187}-\frac{185}{486} (3 x+2)^8+\frac{503}{567} (3 x+2)^7-\frac{259}{729} (3 x+2)^6+\frac{49 (3 x+2)^5}{1215} \]
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Rubi [A] time = 0.0225944, antiderivative size = 56, 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} \[ \frac{100 (3 x+2)^9}{2187}-\frac{185}{486} (3 x+2)^8+\frac{503}{567} (3 x+2)^7-\frac{259}{729} (3 x+2)^6+\frac{49 (3 x+2)^5}{1215} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^4-\frac{518}{81} (2+3 x)^5+\frac{503}{27} (2+3 x)^6-\frac{740}{81} (2+3 x)^7+\frac{100}{81} (2+3 x)^8\right ) \, dx\\ &=\frac{49 (2+3 x)^5}{1215}-\frac{259}{729} (2+3 x)^6+\frac{503}{567} (2+3 x)^7-\frac{185}{486} (2+3 x)^8+\frac{100 (2+3 x)^9}{2187}\\ \end{align*}
Mathematica [A] time = 0.0019102, size = 52, normalized size = 0.93 \[ 900 x^9+\frac{5805 x^8}{2}+\frac{21141 x^7}{7}+115 x^6-\frac{9791 x^5}{5}-1174 x^4+\frac{424 x^3}{3}+384 x^2+144 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 0.8 \begin{align*} 900\,{x}^{9}+{\frac{5805\,{x}^{8}}{2}}+{\frac{21141\,{x}^{7}}{7}}+115\,{x}^{6}-{\frac{9791\,{x}^{5}}{5}}-1174\,{x}^{4}+{\frac{424\,{x}^{3}}{3}}+384\,{x}^{2}+144\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03484, size = 59, normalized size = 1.05 \begin{align*} 900 \, x^{9} + \frac{5805}{2} \, x^{8} + \frac{21141}{7} \, x^{7} + 115 \, x^{6} - \frac{9791}{5} \, x^{5} - 1174 \, x^{4} + \frac{424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31116, size = 135, normalized size = 2.41 \begin{align*} 900 x^{9} + \frac{5805}{2} x^{8} + \frac{21141}{7} x^{7} + 115 x^{6} - \frac{9791}{5} x^{5} - 1174 x^{4} + \frac{424}{3} x^{3} + 384 x^{2} + 144 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065738, size = 49, normalized size = 0.88 \begin{align*} 900 x^{9} + \frac{5805 x^{8}}{2} + \frac{21141 x^{7}}{7} + 115 x^{6} - \frac{9791 x^{5}}{5} - 1174 x^{4} + \frac{424 x^{3}}{3} + 384 x^{2} + 144 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.96286, size = 59, normalized size = 1.05 \begin{align*} 900 \, x^{9} + \frac{5805}{2} \, x^{8} + \frac{21141}{7} \, x^{7} + 115 \, x^{6} - \frac{9791}{5} \, x^{5} - 1174 \, x^{4} + \frac{424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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