Optimal. Leaf size=45 \[ \frac{25}{162 (3 x+2)^4}-\frac{13}{27 (3 x+2)^5}+\frac{4}{27 (3 x+2)^6}-\frac{1}{81 (3 x+2)^7} \]
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Rubi [A] time = 0.0159551, antiderivative size = 45, 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} \[ \frac{25}{162 (3 x+2)^4}-\frac{13}{27 (3 x+2)^5}+\frac{4}{27 (3 x+2)^6}-\frac{1}{81 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx &=\int \left (\frac{7}{27 (2+3 x)^8}-\frac{8}{3 (2+3 x)^7}+\frac{65}{9 (2+3 x)^6}-\frac{50}{27 (2+3 x)^5}\right ) \, dx\\ &=-\frac{1}{81 (2+3 x)^7}+\frac{4}{27 (2+3 x)^6}-\frac{13}{27 (2+3 x)^5}+\frac{25}{162 (2+3 x)^4}\\ \end{align*}
Mathematica [A] time = 0.0093844, size = 26, normalized size = 0.58 \[ \frac{225 x^3+216 x^2+12 x-22}{54 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 38, normalized size = 0.8 \begin{align*} -{\frac{1}{81\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{4}{27\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{13}{27\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{25}{162\, \left ( 2+3\,x \right ) ^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13407, size = 73, normalized size = 1.62 \begin{align*} \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81707, size = 166, normalized size = 3.69 \begin{align*} \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.164313, size = 49, normalized size = 1.09 \begin{align*} \frac{225 x^{3} + 216 x^{2} + 12 x - 22}{118098 x^{7} + 551124 x^{6} + 1102248 x^{5} + 1224720 x^{4} + 816480 x^{3} + 326592 x^{2} + 72576 x + 6912} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.33969, size = 32, normalized size = 0.71 \begin{align*} \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (3 \, x + 2\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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