Optimal. Leaf size=87 \[ \frac {176}{117649 (1-2 x)}-\frac {1040}{117649 (3 x+2)}-\frac {194}{16807 (3 x+2)^2}-\frac {128}{7203 (3 x+2)^3}-\frac {31}{1372 (3 x+2)^4}+\frac {1}{245 (3 x+2)^5}-\frac {2608 \log (1-2 x)}{823543}+\frac {2608 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.04, antiderivative size = 87, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {176}{117649 (1-2 x)}-\frac {1040}{117649 (3 x+2)}-\frac {194}{16807 (3 x+2)^2}-\frac {128}{7203 (3 x+2)^3}-\frac {31}{1372 (3 x+2)^4}+\frac {1}{245 (3 x+2)^5}-\frac {2608 \log (1-2 x)}{823543}+\frac {2608 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^2 (2+3 x)^6} \, dx &=\int \left (\frac {352}{117649 (-1+2 x)^2}-\frac {5216}{823543 (-1+2 x)}-\frac {3}{49 (2+3 x)^6}+\frac {93}{343 (2+3 x)^5}+\frac {384}{2401 (2+3 x)^4}+\frac {1164}{16807 (2+3 x)^3}+\frac {3120}{117649 (2+3 x)^2}+\frac {7824}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {176}{117649 (1-2 x)}+\frac {1}{245 (2+3 x)^5}-\frac {31}{1372 (2+3 x)^4}-\frac {128}{7203 (2+3 x)^3}-\frac {194}{16807 (2+3 x)^2}-\frac {1040}{117649 (2+3 x)}-\frac {2608 \log (1-2 x)}{823543}+\frac {2608 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A] time = 0.07, size = 62, normalized size = 0.71 \[ \frac {-\frac {7 \left (12674880 x^5+34855920 x^4+33741000 x^3+10410810 x^2-3488689 x-2104258\right )}{(2 x-1) (3 x+2)^5}-156480 \log (3-6 x)+156480 \log (3 x+2)}{49412580} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 135, normalized size = 1.55 \[ -\frac {88724160 \, x^{5} + 243991440 \, x^{4} + 236187000 \, x^{3} + 72875670 \, x^{2} - 156480 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 156480 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) - 24420823 \, x - 14729806}{49412580 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 78, normalized size = 0.90 \[ -\frac {176}{117649 \, {\left (2 \, x - 1\right )}} + \frac {12 \, {\left (\frac {3424365}{2 \, x - 1} + \frac {13259400}{{\left (2 \, x - 1\right )}^{2}} + \frac {23152500}{{\left (2 \, x - 1\right )}^{3}} + \frac {15366400}{{\left (2 \, x - 1\right )}^{4}} + 335637\right )}}{4117715 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{5}} + \frac {2608}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.83 \[ -\frac {2608 \ln \left (2 x -1\right )}{823543}+\frac {2608 \ln \left (3 x +2\right )}{823543}+\frac {1}{245 \left (3 x +2\right )^{5}}-\frac {31}{1372 \left (3 x +2\right )^{4}}-\frac {128}{7203 \left (3 x +2\right )^{3}}-\frac {194}{16807 \left (3 x +2\right )^{2}}-\frac {1040}{117649 \left (3 x +2\right )}-\frac {176}{117649 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 76, normalized size = 0.87 \[ -\frac {12674880 \, x^{5} + 34855920 \, x^{4} + 33741000 \, x^{3} + 10410810 \, x^{2} - 3488689 \, x - 2104258}{7058940 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac {2608}{823543} \, \log \left (3 \, x + 2\right ) - \frac {2608}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 66, normalized size = 0.76 \[ \frac {5216\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {1304\,x^5}{352947}+\frac {3586\,x^4}{352947}+\frac {93725\,x^3}{9529569}+\frac {347027\,x^2}{114354828}-\frac {3488689\,x}{3430644840}-\frac {1052129}{1715322420}}{x^6+\frac {17\,x^5}{6}+\frac {25\,x^4}{9}+\frac {20\,x^3}{27}-\frac {40\,x^2}{81}-\frac {88\,x}{243}-\frac {16}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 75, normalized size = 0.86 \[ \frac {- 12674880 x^{5} - 34855920 x^{4} - 33741000 x^{3} - 10410810 x^{2} + 3488689 x + 2104258}{3430644840 x^{6} + 9720160380 x^{5} + 9529569000 x^{4} + 2541218400 x^{3} - 1694145600 x^{2} - 1242373440 x - 225886080} - \frac {2608 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {2608 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
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