Optimal. Leaf size=45 \[ \frac{25}{81 (3 x+2)^2}-\frac{65}{81 (3 x+2)^3}+\frac{2}{9 (3 x+2)^4}-\frac{7}{405 (3 x+2)^5} \]
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Rubi [A] time = 0.0163552, 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} \[ \frac{25}{81 (3 x+2)^2}-\frac{65}{81 (3 x+2)^3}+\frac{2}{9 (3 x+2)^4}-\frac{7}{405 (3 x+2)^5} \]
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)^6} \, dx &=\int \left (\frac{7}{27 (2+3 x)^6}-\frac{8}{3 (2+3 x)^5}+\frac{65}{9 (2+3 x)^4}-\frac{50}{27 (2+3 x)^3}\right ) \, dx\\ &=-\frac{7}{405 (2+3 x)^5}+\frac{2}{9 (2+3 x)^4}-\frac{65}{81 (2+3 x)^3}+\frac{25}{81 (2+3 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0090066, size = 26, normalized size = 0.58 \[ \frac{3375 x^3+3825 x^2+870 x-127}{405 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 38, normalized size = 0.8 \begin{align*} -{\frac{7}{405\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{2}{9\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{65}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{25}{81\, \left ( 2+3\,x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04076, size = 59, normalized size = 1.31 \begin{align*} \frac{3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.89596, size = 131, normalized size = 2.91 \begin{align*} \frac{3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.143193, size = 39, normalized size = 0.87 \begin{align*} \frac{3375 x^{3} + 3825 x^{2} + 870 x - 127}{98415 x^{5} + 328050 x^{4} + 437400 x^{3} + 291600 x^{2} + 97200 x + 12960} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.63445, size = 32, normalized size = 0.71 \begin{align*} \frac{3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \,{\left (3 \, x + 2\right )}^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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