Optimal. Leaf size=65 \[ \frac {319}{2401 (1-2 x)}+\frac {64}{2401 (3 x+2)}+\frac {121}{686 (1-2 x)^2}-\frac {1}{686 (3 x+2)^2}-\frac {829 \log (1-2 x)}{16807}+\frac {829 \log (3 x+2)}{16807} \]
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Rubi [A] time = 0.04, antiderivative size = 65, 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} \[ \frac {319}{2401 (1-2 x)}+\frac {64}{2401 (3 x+2)}+\frac {121}{686 (1-2 x)^2}-\frac {1}{686 (3 x+2)^2}-\frac {829 \log (1-2 x)}{16807}+\frac {829 \log (3 x+2)}{16807} \]
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)^3} \, dx &=\int \left (-\frac {242}{343 (-1+2 x)^3}+\frac {638}{2401 (-1+2 x)^2}-\frac {1658}{16807 (-1+2 x)}+\frac {3}{343 (2+3 x)^3}-\frac {192}{2401 (2+3 x)^2}+\frac {2487}{16807 (2+3 x)}\right ) \, dx\\ &=\frac {121}{686 (1-2 x)^2}+\frac {319}{2401 (1-2 x)}-\frac {1}{686 (2+3 x)^2}+\frac {64}{2401 (2+3 x)}-\frac {829 \log (1-2 x)}{16807}+\frac {829 \log (2+3 x)}{16807}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 48, normalized size = 0.74 \[ \frac {-\frac {7 \left (9948 x^3+2487 x^2-12104 x-6189\right )}{\left (6 x^2+x-2\right )^2}-1658 \log (1-2 x)+1658 \log (3 x+2)}{33614} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 95, normalized size = 1.46 \[ -\frac {69636 \, x^{3} + 17409 \, x^{2} - 1658 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 1658 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 84728 \, x - 43323}{33614 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 46, normalized size = 0.71 \[ -\frac {9948 \, x^{3} + 2487 \, x^{2} - 12104 \, x - 6189}{4802 \, {\left (6 \, x^{2} + x - 2\right )}^{2}} + \frac {829}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {829}{16807} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.83 \[ -\frac {829 \ln \left (2 x -1\right )}{16807}+\frac {829 \ln \left (3 x +2\right )}{16807}-\frac {1}{686 \left (3 x +2\right )^{2}}+\frac {64}{2401 \left (3 x +2\right )}+\frac {121}{686 \left (2 x -1\right )^{2}}-\frac {319}{2401 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 56, normalized size = 0.86 \[ -\frac {9948 \, x^{3} + 2487 \, x^{2} - 12104 \, x - 6189}{4802 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac {829}{16807} \, \log \left (3 \, x + 2\right ) - \frac {829}{16807} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 45, normalized size = 0.69 \[ \frac {1658\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}+\frac {-\frac {829\,x^3}{14406}-\frac {829\,x^2}{57624}+\frac {1513\,x}{21609}+\frac {2063}{57624}}{x^4+\frac {x^3}{3}-\frac {23\,x^2}{36}-\frac {x}{9}+\frac {1}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 54, normalized size = 0.83 \[ - \frac {9948 x^{3} + 2487 x^{2} - 12104 x - 6189}{172872 x^{4} + 57624 x^{3} - 110446 x^{2} - 19208 x + 19208} - \frac {829 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {829 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
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