Optimal. Leaf size=67 \[ -\frac{500}{729 (3 x+2)}+\frac{1900}{729 (3 x+2)^2}-\frac{8285}{2187 (3 x+2)^3}+\frac{4099}{2916 (3 x+2)^4}-\frac{763}{3645 (3 x+2)^5}+\frac{49}{4374 (3 x+2)^6} \]
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Rubi [A] time = 0.0233289, antiderivative size = 67, 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} \[ -\frac{500}{729 (3 x+2)}+\frac{1900}{729 (3 x+2)^2}-\frac{8285}{2187 (3 x+2)^3}+\frac{4099}{2916 (3 x+2)^4}-\frac{763}{3645 (3 x+2)^5}+\frac{49}{4374 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^7} \, dx &=\int \left (-\frac{49}{243 (2+3 x)^7}+\frac{763}{243 (2+3 x)^6}-\frac{4099}{243 (2+3 x)^5}+\frac{8285}{243 (2+3 x)^4}-\frac{3800}{243 (2+3 x)^3}+\frac{500}{243 (2+3 x)^2}\right ) \, dx\\ &=\frac{49}{4374 (2+3 x)^6}-\frac{763}{3645 (2+3 x)^5}+\frac{4099}{2916 (2+3 x)^4}-\frac{8285}{2187 (2+3 x)^3}+\frac{1900}{729 (2+3 x)^2}-\frac{500}{729 (2+3 x)}\\ \end{align*}
Mathematica [A] time = 0.0267871, size = 36, normalized size = 0.54 \[ -\frac{7290000 x^5+15066000 x^4+12249900 x^3+5370435 x^2+1510848 x+233482}{43740 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 56, normalized size = 0.8 \begin{align*}{\frac{49}{4374\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{763}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4099}{2916\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{8285}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1900}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{500}{1458+2187\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03119, size = 80, normalized size = 1.19 \begin{align*} -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50294, size = 211, normalized size = 3.15 \begin{align*} -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.164601, size = 56, normalized size = 0.84 \begin{align*} - \frac{7290000 x^{5} + 15066000 x^{4} + 12249900 x^{3} + 5370435 x^{2} + 1510848 x + 233482}{31886460 x^{6} + 127545840 x^{5} + 212576400 x^{4} + 188956800 x^{3} + 94478400 x^{2} + 25194240 x + 2799360} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.3144, size = 46, normalized size = 0.69 \begin{align*} -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (3 \, x + 2\right )}^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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