Optimal. Leaf size=76 \[ \frac {484}{16807 (1-2 x)}-\frac {1364}{16807 (3 x+2)}-\frac {319}{4802 (3 x+2)^2}+\frac {22}{1029 (3 x+2)^3}-\frac {1}{588 (3 x+2)^4}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (3 x+2)}{117649} \]
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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} \[ \frac {484}{16807 (1-2 x)}-\frac {1364}{16807 (3 x+2)}-\frac {319}{4802 (3 x+2)^2}+\frac {22}{1029 (3 x+2)^3}-\frac {1}{588 (3 x+2)^4}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^5} \, dx &=\int \left (\frac {968}{16807 (-1+2 x)^2}-\frac {8360}{117649 (-1+2 x)}+\frac {1}{49 (2+3 x)^5}-\frac {66}{343 (2+3 x)^4}+\frac {957}{2401 (2+3 x)^3}+\frac {4092}{16807 (2+3 x)^2}+\frac {12540}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {484}{16807 (1-2 x)}-\frac {1}{588 (2+3 x)^4}+\frac {22}{1029 (2+3 x)^3}-\frac {319}{4802 (2+3 x)^2}-\frac {1364}{16807 (2+3 x)}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 59, normalized size = 0.78 \[ \frac {2 \left (-\frac {7 \left (1354320 x^4+2821500 x^3+1724250 x^2+172990 x-83327\right )}{8 (2 x-1) (3 x+2)^4}-6270 \log (1-2 x)+6270 \log (6 x+4)\right )}{352947} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 115, normalized size = 1.51 \[ -\frac {9480240 \, x^{4} + 19750500 \, x^{3} + 12069750 \, x^{2} - 50160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) + 50160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) + 1210930 \, x - 583289}{1411788 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 67, normalized size = 0.88 \[ -\frac {1364}{16807 \, {\left (3 \, x + 2\right )}} + \frac {2904}{117649 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} - \frac {319}{4802 \, {\left (3 \, x + 2\right )}^{2}} + \frac {22}{1029 \, {\left (3 \, x + 2\right )}^{3}} - \frac {1}{588 \, {\left (3 \, x + 2\right )}^{4}} - \frac {4180}{117649} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
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 \[ -\frac {4180 \ln \left (2 x -1\right )}{117649}+\frac {4180 \ln \left (3 x +2\right )}{117649}-\frac {1}{588 \left (3 x +2\right )^{4}}+\frac {22}{1029 \left (3 x +2\right )^{3}}-\frac {319}{4802 \left (3 x +2\right )^{2}}-\frac {1364}{16807 \left (3 x +2\right )}-\frac {484}{16807 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 66, normalized size = 0.87 \[ -\frac {1354320 \, x^{4} + 2821500 \, x^{3} + 1724250 \, x^{2} + 172990 \, x - 83327}{201684 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac {4180}{117649} \, \log \left (3 \, x + 2\right ) - \frac {4180}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 57, normalized size = 0.75 \[ \frac {8360\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {\frac {2090\,x^4}{50421}+\frac {26125\,x^3}{302526}+\frac {287375\,x^2}{5445468}+\frac {86495\,x}{16336404}-\frac {83327}{32672808}}{-x^5-\frac {13\,x^4}{6}-\frac {4\,x^3}{3}+\frac {4\,x^2}{27}+\frac {32\,x}{81}+\frac {8}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 65, normalized size = 0.86 \[ \frac {- 1354320 x^{4} - 2821500 x^{3} - 1724250 x^{2} - 172990 x + 83327}{32672808 x^{5} + 70791084 x^{4} + 43563744 x^{3} - 4840416 x^{2} - 12907776 x - 3226944} - \frac {4180 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {4180 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
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