Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^{13}}{3159}-\frac{185}{729} (3 x+2)^{12}+\frac{503}{891} (3 x+2)^{11}-\frac{259 (3 x+2)^{10}}{1215}+\frac{49 (3 x+2)^9}{2187} \]
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Rubi [A] time = 0.0313688, 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} \[ \frac{100 (3 x+2)^{13}}{3159}-\frac{185}{729} (3 x+2)^{12}+\frac{503}{891} (3 x+2)^{11}-\frac{259 (3 x+2)^{10}}{1215}+\frac{49 (3 x+2)^9}{2187} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^8-\frac{518}{81} (2+3 x)^9+\frac{503}{27} (2+3 x)^{10}-\frac{740}{81} (2+3 x)^{11}+\frac{100}{81} (2+3 x)^{12}\right ) \, dx\\ &=\frac{49 (2+3 x)^9}{2187}-\frac{259 (2+3 x)^{10}}{1215}+\frac{503}{891} (2+3 x)^{11}-\frac{185}{729} (2+3 x)^{12}+\frac{100 (2+3 x)^{13}}{3159}\\ \end{align*}
Mathematica [A] time = 0.0029319, size = 74, normalized size = 1.32 \[ \frac{656100 x^{13}}{13}+302535 x^{12}+\frac{8477541 x^{11}}{11}+\frac{5207733 x^{10}}{5}+697905 x^9+6858 x^8-384336 x^7-298240 x^6-\frac{338336 x^5}{5}+40640 x^4+\frac{111616 x^3}{3}+13056 x^2+2304 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 65, normalized size = 1.2 \begin{align*}{\frac{656100\,{x}^{13}}{13}}+302535\,{x}^{12}+{\frac{8477541\,{x}^{11}}{11}}+{\frac{5207733\,{x}^{10}}{5}}+697905\,{x}^{9}+6858\,{x}^{8}-384336\,{x}^{7}-298240\,{x}^{6}-{\frac{338336\,{x}^{5}}{5}}+40640\,{x}^{4}+{\frac{111616\,{x}^{3}}{3}}+13056\,{x}^{2}+2304\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06466, size = 86, normalized size = 1.54 \begin{align*} \frac{656100}{13} \, x^{13} + 302535 \, x^{12} + \frac{8477541}{11} \, x^{11} + \frac{5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac{338336}{5} \, x^{5} + 40640 \, x^{4} + \frac{111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32728, size = 240, normalized size = 4.29 \begin{align*} \frac{656100}{13} x^{13} + 302535 x^{12} + \frac{8477541}{11} x^{11} + \frac{5207733}{5} x^{10} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac{338336}{5} x^{5} + 40640 x^{4} + \frac{111616}{3} x^{3} + 13056 x^{2} + 2304 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.073572, size = 71, normalized size = 1.27 \begin{align*} \frac{656100 x^{13}}{13} + 302535 x^{12} + \frac{8477541 x^{11}}{11} + \frac{5207733 x^{10}}{5} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac{338336 x^{5}}{5} + 40640 x^{4} + \frac{111616 x^{3}}{3} + 13056 x^{2} + 2304 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.87469, size = 86, normalized size = 1.54 \begin{align*} \frac{656100}{13} \, x^{13} + 302535 \, x^{12} + \frac{8477541}{11} \, x^{11} + \frac{5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac{338336}{5} \, x^{5} + 40640 \, x^{4} + \frac{111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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