Optimal. Leaf size=45 \[ -\frac{10}{81 (3 x+2)^2}+\frac{16}{27 (3 x+2)^3}-\frac{91}{108 (3 x+2)^4}+\frac{49}{405 (3 x+2)^5} \]
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Rubi [A] time = 0.0163791, 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} \[ -\frac{10}{81 (3 x+2)^2}+\frac{16}{27 (3 x+2)^3}-\frac{91}{108 (3 x+2)^4}+\frac{49}{405 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx &=\int \left (-\frac{49}{27 (2+3 x)^6}+\frac{91}{9 (2+3 x)^5}-\frac{16}{3 (2+3 x)^4}+\frac{20}{27 (2+3 x)^3}\right ) \, dx\\ &=\frac{49}{405 (2+3 x)^5}-\frac{91}{108 (2+3 x)^4}+\frac{16}{27 (2+3 x)^3}-\frac{10}{81 (2+3 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0104485, size = 26, normalized size = 0.58 \[ -\frac{1800 x^3+720 x^2-75 x+98}{540 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 38, normalized size = 0.8 \begin{align*}{\frac{49}{405\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{91}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{16}{27\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{10}{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 = 1.13272, size = 59, normalized size = 1.31 \begin{align*} -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\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 = 1.56981, size = 128, normalized size = 2.84 \begin{align*} -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\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 = 0.141443, size = 41, normalized size = 0.91 \begin{align*} - \frac{1800 x^{3} + 720 x^{2} - 75 x + 98}{131220 x^{5} + 437400 x^{4} + 583200 x^{3} + 388800 x^{2} + 129600 x + 17280} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.17067, size = 32, normalized size = 0.71 \begin{align*} -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\left (3 \, x + 2\right )}^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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