Optimal. Leaf size=76 \[ \frac {1364}{16807 (1-2 x)}-\frac {829}{16807 (3 x+2)}+\frac {121}{2401 (1-2 x)^2}+\frac {32}{2401 (3 x+2)^2}-\frac {1}{1029 (3 x+2)^3}-\frac {5750 \log (1-2 x)}{117649}+\frac {5750 \log (3 x+2)}{117649} \]
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Rubi [A] time = 0.04, antiderivative size = 76, normalized size of antiderivative = 1.00, 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} \[ \frac {1364}{16807 (1-2 x)}-\frac {829}{16807 (3 x+2)}+\frac {121}{2401 (1-2 x)^2}+\frac {32}{2401 (3 x+2)^2}-\frac {1}{1029 (3 x+2)^3}-\frac {5750 \log (1-2 x)}{117649}+\frac {5750 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^3 (2+3 x)^4} \, dx &=\int \left (-\frac {484}{2401 (-1+2 x)^3}+\frac {2728}{16807 (-1+2 x)^2}-\frac {11500}{117649 (-1+2 x)}+\frac {3}{343 (2+3 x)^4}-\frac {192}{2401 (2+3 x)^3}+\frac {2487}{16807 (2+3 x)^2}+\frac {17250}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {121}{2401 (1-2 x)^2}+\frac {1364}{16807 (1-2 x)}-\frac {1}{1029 (2+3 x)^3}+\frac {32}{2401 (2+3 x)^2}-\frac {829}{16807 (2+3 x)}-\frac {5750 \log (1-2 x)}{117649}+\frac {5750 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 57, normalized size = 0.75 \[ \frac {\frac {7 \left (-310500 x^4-284625 x^3+117875 x^2+180100 x+44411\right )}{(1-2 x)^2 (3 x+2)^3}-17250 \log (1-2 x)+17250 \log (6 x+4)}{352947} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 115, normalized size = 1.51 \[ -\frac {2173500 \, x^{4} + 1992375 \, x^{3} - 825125 \, x^{2} - 17250 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 17250 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 1260700 \, x - 310877}{352947 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 55, normalized size = 0.72 \[ -\frac {310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \, {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {5750}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {5750}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 63, normalized size = 0.83 \[ -\frac {5750 \ln \left (2 x -1\right )}{117649}+\frac {5750 \ln \left (3 x +2\right )}{117649}-\frac {1}{1029 \left (3 x +2\right )^{3}}+\frac {32}{2401 \left (3 x +2\right )^{2}}-\frac {829}{16807 \left (3 x +2\right )}+\frac {121}{2401 \left (2 x -1\right )^{2}}-\frac {1364}{16807 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 66, normalized size = 0.87 \[ -\frac {310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac {5750}{117649} \, \log \left (3 \, x + 2\right ) - \frac {5750}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 53, normalized size = 0.70 \[ \frac {11500\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {-\frac {2875\,x^4}{50421}-\frac {31625\,x^3}{605052}+\frac {117875\,x^2}{5445468}+\frac {45025\,x}{1361367}+\frac {44411}{5445468}}{x^5+x^4-\frac {5\,x^3}{12}-\frac {29\,x^2}{54}+\frac {x}{27}+\frac {2}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 65, normalized size = 0.86 \[ - \frac {310500 x^{4} + 284625 x^{3} - 117875 x^{2} - 180100 x - 44411}{5445468 x^{5} + 5445468 x^{4} - 2268945 x^{3} - 2924418 x^{2} + 201684 x + 403368} - \frac {5750 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {5750 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
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