Optimal. Leaf size=97 \[ -\frac {1615625}{3 x+2}-\frac {378125}{5 x+3}-\frac {138875}{(3 x+2)^2}-\frac {46475}{3 (3 x+2)^3}-\frac {1870}{(3 x+2)^4}-\frac {1133}{5 (3 x+2)^5}-\frac {77}{3 (3 x+2)^6}-\frac {7}{3 (3 x+2)^7}+9212500 \log (3 x+2)-9212500 \log (5 x+3) \]
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Rubi [A] time = 0.05, antiderivative size = 97, 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} \[ -\frac {1615625}{3 x+2}-\frac {378125}{5 x+3}-\frac {138875}{(3 x+2)^2}-\frac {46475}{3 (3 x+2)^3}-\frac {1870}{(3 x+2)^4}-\frac {1133}{5 (3 x+2)^5}-\frac {77}{3 (3 x+2)^6}-\frac {7}{3 (3 x+2)^7}+9212500 \log (3 x+2)-9212500 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x)^8 (3+5 x)^2} \, dx &=\int \left (\frac {49}{(2+3 x)^8}+\frac {462}{(2+3 x)^7}+\frac {3399}{(2+3 x)^6}+\frac {22440}{(2+3 x)^5}+\frac {139425}{(2+3 x)^4}+\frac {833250}{(2+3 x)^3}+\frac {4846875}{(2+3 x)^2}+\frac {27637500}{2+3 x}+\frac {1890625}{(3+5 x)^2}-\frac {46062500}{3+5 x}\right ) \, dx\\ &=-\frac {7}{3 (2+3 x)^7}-\frac {77}{3 (2+3 x)^6}-\frac {1133}{5 (2+3 x)^5}-\frac {1870}{(2+3 x)^4}-\frac {46475}{3 (2+3 x)^3}-\frac {138875}{(2+3 x)^2}-\frac {1615625}{2+3 x}-\frac {378125}{3+5 x}+9212500 \log (2+3 x)-9212500 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.15, size = 99, normalized size = 1.02 \[ -\frac {1615625}{3 x+2}-\frac {378125}{5 x+3}-\frac {138875}{(3 x+2)^2}-\frac {46475}{3 (3 x+2)^3}-\frac {1870}{(3 x+2)^4}-\frac {1133}{5 (3 x+2)^5}-\frac {77}{3 (3 x+2)^6}-\frac {7}{3 (3 x+2)^7}+9212500 \log (5 (3 x+2))-9212500 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 175, normalized size = 1.80 \[ -\frac {100738687500 \, x^{7} + 466755918750 \, x^{6} + 926721303750 \, x^{5} + 1022059900125 \, x^{4} + 676227617505 \, x^{3} + 268408563588 \, x^{2} + 138187500 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )} \log \left (5 \, x + 3\right ) - 138187500 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )} \log \left (3 \, x + 2\right ) + 59178013234 \, x + 5590850403}{15 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 94, normalized size = 0.97 \[ -\frac {378125}{5 \, x + 3} + \frac {625 \, {\left (\frac {120779019}{5 \, x + 3} + \frac {110006829}{{\left (5 \, x + 3\right )}^{2}} + \frac {54129465}{{\left (5 \, x + 3\right )}^{3}} + \frac {15246900}{{\left (5 \, x + 3\right )}^{4}} + \frac {2349450}{{\left (5 \, x + 3\right )}^{5}} + \frac {157100}{{\left (5 \, x + 3\right )}^{6}} + 55800576\right )}}{{\left (\frac {1}{5 \, x + 3} + 3\right )}^{7}} + 9212500 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 90, normalized size = 0.93 \[ 9212500 \ln \left (3 x +2\right )-9212500 \ln \left (5 x +3\right )-\frac {7}{3 \left (3 x +2\right )^{7}}-\frac {77}{3 \left (3 x +2\right )^{6}}-\frac {1133}{5 \left (3 x +2\right )^{5}}-\frac {1870}{\left (3 x +2\right )^{4}}-\frac {46475}{3 \left (3 x +2\right )^{3}}-\frac {138875}{\left (3 x +2\right )^{2}}-\frac {1615625}{3 x +2}-\frac {378125}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 96, normalized size = 0.99 \[ -\frac {100738687500 \, x^{7} + 466755918750 \, x^{6} + 926721303750 \, x^{5} + 1022059900125 \, x^{4} + 676227617505 \, x^{3} + 268408563588 \, x^{2} + 59178013234 \, x + 5590850403}{15 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )}} - 9212500 \, \log \left (5 \, x + 3\right ) + 9212500 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 86, normalized size = 0.89 \[ 18425000\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {1842500\,x^7}{3}+\frac {25610750\,x^6}{9}+\frac {457640150\,x^5}{81}+\frac {1514162815\,x^4}{243}+\frac {1669697821\,x^3}{405}+\frac {29823173732\,x^2}{18225}+\frac {59178013234\,x}{164025}+\frac {1863616801}{54675}}{x^8+\frac {79\,x^7}{15}+\frac {182\,x^6}{15}+\frac {2156\,x^5}{135}+\frac {1064\,x^4}{81}+\frac {560\,x^3}{81}+\frac {8288\,x^2}{3645}+\frac {4672\,x}{10935}+\frac {128}{3645}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 94, normalized size = 0.97 \[ \frac {- 100738687500 x^{7} - 466755918750 x^{6} - 926721303750 x^{5} - 1022059900125 x^{4} - 676227617505 x^{3} - 268408563588 x^{2} - 59178013234 x - 5590850403}{164025 x^{8} + 863865 x^{7} + 1990170 x^{6} + 2619540 x^{5} + 2154600 x^{4} + 1134000 x^{3} + 372960 x^{2} + 70080 x + 5760} - 9212500 \log {\left (x + \frac {3}{5} \right )} + 9212500 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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