Optimal. Leaf size=78 \[ \frac{1000}{2187 (3 x+2)}-\frac{1850}{729 (3 x+2)^2}+\frac{14390}{2187 (3 x+2)^3}-\frac{66193}{8748 (3 x+2)^4}+\frac{10073}{3645 (3 x+2)^5}-\frac{1813}{4374 (3 x+2)^6}+\frac{49}{2187 (3 x+2)^7} \]
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Rubi [A] time = 0.0271129, antiderivative size = 78, 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} \[ \frac{1000}{2187 (3 x+2)}-\frac{1850}{729 (3 x+2)^2}+\frac{14390}{2187 (3 x+2)^3}-\frac{66193}{8748 (3 x+2)^4}+\frac{10073}{3645 (3 x+2)^5}-\frac{1813}{4374 (3 x+2)^6}+\frac{49}{2187 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^8} \, dx &=\int \left (-\frac{343}{729 (2+3 x)^8}+\frac{1813}{243 (2+3 x)^7}-\frac{10073}{243 (2+3 x)^6}+\frac{66193}{729 (2+3 x)^5}-\frac{14390}{243 (2+3 x)^4}+\frac{3700}{243 (2+3 x)^3}-\frac{1000}{729 (2+3 x)^2}\right ) \, dx\\ &=\frac{49}{2187 (2+3 x)^7}-\frac{1813}{4374 (2+3 x)^6}+\frac{10073}{3645 (2+3 x)^5}-\frac{66193}{8748 (2+3 x)^4}+\frac{14390}{2187 (2+3 x)^3}-\frac{1850}{729 (2+3 x)^2}+\frac{1000}{2187 (2+3 x)}\\ \end{align*}
Mathematica [A] time = 0.0113472, size = 41, normalized size = 0.53 \[ \frac{14580000 x^6+31347000 x^5+30601800 x^4+19748745 x^3+8660574 x^2+1990182 x+133304}{43740 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 65, normalized size = 0.8 \begin{align*}{\frac{49}{2187\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{1813}{4374\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{10073}{3645\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{66193}{8748\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{14390}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1850}{729\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1000}{4374+6561\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13536, size = 93, normalized size = 1.19 \begin{align*} \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\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 = 1.465, size = 255, normalized size = 3.27 \begin{align*} \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\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 = 0.181692, size = 65, normalized size = 0.83 \begin{align*} \frac{14580000 x^{6} + 31347000 x^{5} + 30601800 x^{4} + 19748745 x^{3} + 8660574 x^{2} + 1990182 x + 133304}{95659380 x^{7} + 446410440 x^{6} + 892820880 x^{5} + 992023200 x^{4} + 661348800 x^{3} + 264539520 x^{2} + 58786560 x + 5598720} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.50047, size = 53, normalized size = 0.68 \begin{align*} \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\left (3 \, x + 2\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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