Optimal. Leaf size=109 \[ \frac{3872}{5764801 (1-2 x)}-\frac{4048}{823543 (3 x+2)}-\frac{5632}{823543 (3 x+2)^2}-\frac{4180}{352947 (3 x+2)^3}-\frac{341}{16807 (3 x+2)^4}-\frac{319}{12005 (3 x+2)^5}+\frac{11}{1029 (3 x+2)^6}-\frac{1}{1029 (3 x+2)^7}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (3 x+2)}{40353607} \]
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Rubi [A] time = 0.057644, antiderivative size = 109, 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} \[ \frac{3872}{5764801 (1-2 x)}-\frac{4048}{823543 (3 x+2)}-\frac{5632}{823543 (3 x+2)^2}-\frac{4180}{352947 (3 x+2)^3}-\frac{341}{16807 (3 x+2)^4}-\frac{319}{12005 (3 x+2)^5}+\frac{11}{1029 (3 x+2)^6}-\frac{1}{1029 (3 x+2)^7}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (3 x+2)}{40353607} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx &=\int \left (\frac{7744}{5764801 (-1+2 x)^2}-\frac{136576}{40353607 (-1+2 x)}+\frac{1}{49 (2+3 x)^8}-\frac{66}{343 (2+3 x)^7}+\frac{957}{2401 (2+3 x)^6}+\frac{4092}{16807 (2+3 x)^5}+\frac{12540}{117649 (2+3 x)^4}+\frac{33792}{823543 (2+3 x)^3}+\frac{12144}{823543 (2+3 x)^2}+\frac{204864}{40353607 (2+3 x)}\right ) \, dx\\ &=\frac{3872}{5764801 (1-2 x)}-\frac{1}{1029 (2+3 x)^7}+\frac{11}{1029 (2+3 x)^6}-\frac{319}{12005 (2+3 x)^5}-\frac{341}{16807 (2+3 x)^4}-\frac{4180}{352947 (2+3 x)^3}-\frac{5632}{823543 (2+3 x)^2}-\frac{4048}{823543 (2+3 x)}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (2+3 x)}{40353607}\\ \end{align*}
Mathematica [A] time = 0.0773825, size = 74, normalized size = 0.68 \[ \frac{16 \left (-\frac{7 \left (746729280 x^7+3049144560 x^6+5057708040 x^5+4176440730 x^4+1495734471 x^3-183177225 x^2-327016403 x-76539293\right )}{16 (2 x-1) (3 x+2)^7}-64020 \log (1-2 x)+64020 \log (6 x+4)\right )}{605304105} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 90, normalized size = 0.8 \begin{align*} -{\frac{3872}{11529602\,x-5764801}}-{\frac{68288\,\ln \left ( 2\,x-1 \right ) }{40353607}}-{\frac{1}{1029\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{11}{1029\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{319}{12005\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{341}{16807\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{4180}{352947\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{5632}{823543\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{4048}{1647086+2470629\,x}}+{\frac{68288\,\ln \left ( 2+3\,x \right ) }{40353607}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05825, size = 130, normalized size = 1.19 \begin{align*} -\frac{746729280 \, x^{7} + 3049144560 \, x^{6} + 5057708040 \, x^{5} + 4176440730 \, x^{4} + 1495734471 \, x^{3} - 183177225 \, x^{2} - 327016403 \, x - 76539293}{86472015 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} + \frac{68288}{40353607} \, \log \left (3 \, x + 2\right ) - \frac{68288}{40353607} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2972, size = 645, normalized size = 5.92 \begin{align*} -\frac{5227104960 \, x^{7} + 21344011920 \, x^{6} + 35403956280 \, x^{5} + 29235085110 \, x^{4} + 10470141297 \, x^{3} - 1282240575 \, x^{2} - 1024320 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (3 \, x + 2\right ) + 1024320 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (2 \, x - 1\right ) - 2289114821 \, x - 535775051}{605304105 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.223706, size = 95, normalized size = 0.87 \begin{align*} - \frac{746729280 x^{7} + 3049144560 x^{6} + 5057708040 x^{5} + 4176440730 x^{4} + 1495734471 x^{3} - 183177225 x^{2} - 327016403 x - 76539293}{378228593610 x^{8} + 1575952473375 x^{7} + 2647600155270 x^{6} + 2157303830220 x^{5} + 653728433400 x^{4} - 261491373360 x^{3} - 290545970400 x^{2} - 94081552320 x - 11068417920} - \frac{68288 \log{\left (x - \frac{1}{2} \right )}}{40353607} + \frac{68288 \log{\left (x + \frac{2}{3} \right )}}{40353607} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.85019, size = 130, normalized size = 1.19 \begin{align*} -\frac{3872}{5764801 \,{\left (2 \, x - 1\right )}} + \frac{16 \,{\left (\frac{6995041011}{2 \, x - 1} + \frac{43950177747}{{\left (2 \, x - 1\right )}^{2}} + \frac{148454802405}{{\left (2 \, x - 1\right )}^{3}} + \frac{284722344900}{{\left (2 \, x - 1\right )}^{4}} + \frac{294251913900}{{\left (2 \, x - 1\right )}^{5}} + \frac{128036230210}{{\left (2 \, x - 1\right )}^{6}} + 466999587\right )}}{1412376245 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{7}} + \frac{68288}{40353607} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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