Optimal. Leaf size=97 \[ -\frac {3584625}{3 x+2}-\frac {831875}{5 x+3}-\frac {308550}{(3 x+2)^2}-\frac {34485}{(3 x+2)^3}-\frac {8349}{2 (3 x+2)^4}-\frac {2541}{5 (3 x+2)^5}-\frac {1568}{27 (3 x+2)^6}-\frac {49}{9 (3 x+2)^7}+20418750 \log (3 x+2)-20418750 \log (5 x+3) \]
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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} \[ -\frac {3584625}{3 x+2}-\frac {831875}{5 x+3}-\frac {308550}{(3 x+2)^2}-\frac {34485}{(3 x+2)^3}-\frac {8349}{2 (3 x+2)^4}-\frac {2541}{5 (3 x+2)^5}-\frac {1568}{27 (3 x+2)^6}-\frac {49}{9 (3 x+2)^7}+20418750 \log (3 x+2)-20418750 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^8 (3+5 x)^2} \, dx &=\int \left (\frac {343}{3 (2+3 x)^8}+\frac {3136}{3 (2+3 x)^7}+\frac {7623}{(2+3 x)^6}+\frac {50094}{(2+3 x)^5}+\frac {310365}{(2+3 x)^4}+\frac {1851300}{(2+3 x)^3}+\frac {10753875}{(2+3 x)^2}+\frac {61256250}{2+3 x}+\frac {4159375}{(3+5 x)^2}-\frac {102093750}{3+5 x}\right ) \, dx\\ &=-\frac {49}{9 (2+3 x)^7}-\frac {1568}{27 (2+3 x)^6}-\frac {2541}{5 (2+3 x)^5}-\frac {8349}{2 (2+3 x)^4}-\frac {34485}{(2+3 x)^3}-\frac {308550}{(2+3 x)^2}-\frac {3584625}{2+3 x}-\frac {831875}{3+5 x}+20418750 \log (2+3 x)-20418750 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.18, size = 99, normalized size = 1.02 \[ -\frac {3584625}{3 x+2}-\frac {831875}{5 x+3}-\frac {308550}{(3 x+2)^2}-\frac {34485}{(3 x+2)^3}-\frac {8349}{2 (3 x+2)^4}-\frac {2541}{5 (3 x+2)^5}-\frac {1568}{27 (3 x+2)^6}-\frac {49}{9 (3 x+2)^7}+20418750 \log (5 (3 x+2))-20418750 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 175, normalized size = 1.80 \[ -\frac {4019022562500 \, x^{7} + 18621471206250 \, x^{6} + 36972030521250 \, x^{5} + 40775613627375 \, x^{4} + 26978454053595 \, x^{3} + 10708299857748 \, x^{2} + 5513062500 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )} \log \left (5 \, x + 3\right ) - 5513062500 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )} \log \left (3 \, x + 2\right ) + 2360937751874 \, x + 223049897418}{270 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 94, normalized size = 0.97 \[ -\frac {831875}{5 \, x + 3} + \frac {625 \, {\left (\frac {537521373}{5 \, x + 3} + \frac {489712095}{{\left (5 \, x + 3\right )}^{2}} + \frac {241051911}{{\left (5 \, x + 3\right )}^{3}} + \frac {67932770}{{\left (5 \, x + 3\right )}^{4}} + \frac {10476370}{{\left (5 \, x + 3\right )}^{5}} + \frac {701580}{{\left (5 \, x + 3\right )}^{6}} + 248285331\right )}}{2 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{7}} + 20418750 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
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 \[ 20418750 \ln \left (3 x +2\right )-20418750 \ln \left (5 x +3\right )-\frac {49}{9 \left (3 x +2\right )^{7}}-\frac {1568}{27 \left (3 x +2\right )^{6}}-\frac {2541}{5 \left (3 x +2\right )^{5}}-\frac {8349}{2 \left (3 x +2\right )^{4}}-\frac {34485}{\left (3 x +2\right )^{3}}-\frac {308550}{\left (3 x +2\right )^{2}}-\frac {3584625}{3 x +2}-\frac {831875}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 96, normalized size = 0.99 \[ -\frac {4019022562500 \, x^{7} + 18621471206250 \, x^{6} + 36972030521250 \, x^{5} + 40775613627375 \, x^{4} + 26978454053595 \, x^{3} + 10708299857748 \, x^{2} + 2360937751874 \, x + 223049897418}{270 \, {\left (10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right )}} - 20418750 \, \log \left (5 \, x + 3\right ) + 20418750 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.16, size = 86, normalized size = 0.89 \[ 40837500\,\mathrm {atanh}\left (30\,x+19\right )-\frac {1361250\,x^7+6307125\,x^6+\frac {37567475\,x^5}{3}+\frac {248593895\,x^4}{18}+\frac {274129493\,x^3}{30}+\frac {1784716642958\,x^2}{492075}+\frac {1180468875937\,x}{1476225}+\frac {37174982903}{492075}}{x^8+\frac {79\,x^7}{15}+\frac {182\,x^6}{15}+\frac {2156\,x^5}{135}+\frac {1064\,x^4}{81}+\frac {560\,x^3}{81}+\frac {8288\,x^2}{3645}+\frac {4672\,x}{10935}+\frac {128}{3645}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 92, normalized size = 0.95 \[ - \frac {4019022562500 x^{7} + 18621471206250 x^{6} + 36972030521250 x^{5} + 40775613627375 x^{4} + 26978454053595 x^{3} + 10708299857748 x^{2} + 2360937751874 x + 223049897418}{2952450 x^{8} + 15549570 x^{7} + 35823060 x^{6} + 47151720 x^{5} + 38782800 x^{4} + 20412000 x^{3} + 6713280 x^{2} + 1261440 x + 103680} - 20418750 \log {\left (x + \frac {3}{5} \right )} + 20418750 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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