Integrand size = 22, antiderivative size = 80 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=\frac {99648703}{2048 (1-2 x)^2}-\frac {389535839}{1024 (1-2 x)}-\frac {48280011 x}{64}-\frac {190742391 x^2}{512}-\frac {25895367 x^3}{128}-\frac {12299769 x^4}{128}-\frac {2798631 x^5}{80}-\frac {268515 x^6}{32}-\frac {54675 x^7}{56}-\frac {84589631}{128} \log (1-2 x) \]
99648703/2048/(1-2*x)^2-389535839/1024/(1-2*x)-48280011/64*x-190742391/512 *x^2-25895367/128*x^3-12299769/128*x^4-2798631/80*x^5-268515/32*x^6-54675/ 56*x^7-84589631/128*ln(1-2*x)
Time = 0.02 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=-\frac {-1533057471+17964456304 x-41720946264 x^2+15497514480 x^3+6962248440 x^4+4120214112 x^5+2265332832 x^6+961797888 x^7+265744800 x^8+34992000 x^9+5921274170 (1-2 x)^2 \log (1-2 x)}{8960 (1-2 x)^2} \]
-1/8960*(-1533057471 + 17964456304*x - 41720946264*x^2 + 15497514480*x^3 + 6962248440*x^4 + 4120214112*x^5 + 2265332832*x^6 + 961797888*x^7 + 265744 800*x^8 + 34992000*x^9 + 5921274170*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2
Time = 0.21 (sec) , antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {99, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {(3 x+2)^7 (5 x+3)^2}{(1-2 x)^3} \, dx\) |
| \(\Big \downarrow \) 99 |
| \(\displaystyle \int \left (-\frac {54675 x^6}{8}-\frac {805545 x^5}{16}-\frac {2798631 x^4}{16}-\frac {12299769 x^3}{32}-\frac {77686101 x^2}{128}-\frac {190742391 x}{256}-\frac {84589631}{64 (2 x-1)}-\frac {389535839}{512 (2 x-1)^2}-\frac {99648703}{512 (2 x-1)^3}-\frac {48280011}{64}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {54675 x^7}{56}-\frac {268515 x^6}{32}-\frac {2798631 x^5}{80}-\frac {12299769 x^4}{128}-\frac {25895367 x^3}{128}-\frac {190742391 x^2}{512}-\frac {48280011 x}{64}-\frac {389535839}{1024 (1-2 x)}+\frac {99648703}{2048 (1-2 x)^2}-\frac {84589631}{128} \log (1-2 x)\) |
99648703/(2048*(1 - 2*x)^2) - 389535839/(1024*(1 - 2*x)) - (48280011*x)/64 - (190742391*x^2)/512 - (25895367*x^3)/128 - (12299769*x^4)/128 - (279863 1*x^5)/80 - (268515*x^6)/32 - (54675*x^7)/56 - (84589631*Log[1 - 2*x])/128
3.17.45.3.1 Defintions of rubi rules used
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] && (IntegerQ[p] | | (GtQ[m, 0] && GeQ[n, -1]))
Time = 2.73 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71
| method | result | size |
| risch | \(-\frac {54675 x^{7}}{56}-\frac {268515 x^{6}}{32}-\frac {2798631 x^{5}}{80}-\frac {12299769 x^{4}}{128}-\frac {25895367 x^{3}}{128}-\frac {190742391 x^{2}}{512}-\frac {48280011 x}{64}+\frac {\frac {389535839 x}{512}-\frac {679422975}{2048}}{\left (-1+2 x \right )^{2}}-\frac {84589631 \ln \left (-1+2 x \right )}{128}\) | \(57\) |
| default | \(-\frac {54675 x^{7}}{56}-\frac {268515 x^{6}}{32}-\frac {2798631 x^{5}}{80}-\frac {12299769 x^{4}}{128}-\frac {25895367 x^{3}}{128}-\frac {190742391 x^{2}}{512}-\frac {48280011 x}{64}-\frac {84589631 \ln \left (-1+2 x \right )}{128}+\frac {389535839}{1024 \left (-1+2 x \right )}+\frac {99648703}{2048 \left (-1+2 x \right )^{2}}\) | \(61\) |
| norman | \(\frac {-\frac {84515903}{64} x +\frac {254205117}{64} x^{2}-\frac {27674133}{16} x^{3}-\frac {24865173}{32} x^{4}-\frac {18393813}{40} x^{5}-\frac {10113093}{40} x^{6}-\frac {3757023}{35} x^{7}-\frac {1660905}{56} x^{8}-\frac {54675}{14} x^{9}}{\left (-1+2 x \right )^{2}}-\frac {84589631 \ln \left (-1+2 x \right )}{128}\) | \(62\) |
| parallelrisch | \(-\frac {17496000 x^{9}+132872400 x^{8}+480898944 x^{7}+1132666416 x^{6}+2060107056 x^{5}+3481124220 x^{4}+11842548340 \ln \left (x -\frac {1}{2}\right ) x^{2}+7748757240 x^{3}-11842548340 \ln \left (x -\frac {1}{2}\right ) x -17794358190 x^{2}+2960637085 \ln \left (x -\frac {1}{2}\right )+5916113210 x}{4480 \left (-1+2 x \right )^{2}}\) | \(76\) |
| meijerg | \(\frac {576 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {7968 x^{2}}{\left (1-2 x \right )^{2}}-\frac {12244 x \left (-18 x +6\right )}{3 \left (1-2 x \right )^{2}}-\frac {84589631 \ln \left (1-2 x \right )}{128}-\frac {21945 x \left (16 x^{2}-36 x +12\right )}{2 \left (1-2 x \right )^{2}}-\frac {20223 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{4 \left (1-2 x \right )^{2}}-\frac {103509 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{16 \left (1-2 x \right )^{2}}-\frac {90801 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{128 \left (1-2 x \right )^{2}}-\frac {836163 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{5120 \left (1-2 x \right )^{2}}-\frac {891 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{64 \left (1-2 x \right )^{2}}-\frac {10935 x \left (2560 x^{8}+1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{7168 \left (1-2 x \right )^{2}}\) | \(297\) |
-54675/56*x^7-268515/32*x^6-2798631/80*x^5-12299769/128*x^4-25895367/128*x ^3-190742391/512*x^2-48280011/64*x+4*(389535839/2048*x-679422975/8192)/(-1 +2*x)^2-84589631/128*ln(-1+2*x)
Time = 0.21 (sec) , antiderivative size = 77, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=-\frac {279936000 \, x^{9} + 2125958400 \, x^{8} + 7694383104 \, x^{7} + 18122662656 \, x^{6} + 32961712896 \, x^{5} + 55697987520 \, x^{4} + 123980115840 \, x^{3} - 189590514540 \, x^{2} + 47370193360 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 461405140 \, x + 23779804125}{71680 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
-1/71680*(279936000*x^9 + 2125958400*x^8 + 7694383104*x^7 + 18122662656*x^ 6 + 32961712896*x^5 + 55697987520*x^4 + 123980115840*x^3 - 189590514540*x^ 2 + 47370193360*(4*x^2 - 4*x + 1)*log(2*x - 1) - 461405140*x + 23779804125 )/(4*x^2 - 4*x + 1)
Time = 0.08 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=- \frac {54675 x^{7}}{56} - \frac {268515 x^{6}}{32} - \frac {2798631 x^{5}}{80} - \frac {12299769 x^{4}}{128} - \frac {25895367 x^{3}}{128} - \frac {190742391 x^{2}}{512} - \frac {48280011 x}{64} - \frac {679422975 - 1558143356 x}{8192 x^{2} - 8192 x + 2048} - \frac {84589631 \log {\left (2 x - 1 \right )}}{128} \]
-54675*x**7/56 - 268515*x**6/32 - 2798631*x**5/80 - 12299769*x**4/128 - 25 895367*x**3/128 - 190742391*x**2/512 - 48280011*x/64 - (679422975 - 155814 3356*x)/(8192*x**2 - 8192*x + 2048) - 84589631*log(2*x - 1)/128
Time = 0.19 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.76 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=-\frac {54675}{56} \, x^{7} - \frac {268515}{32} \, x^{6} - \frac {2798631}{80} \, x^{5} - \frac {12299769}{128} \, x^{4} - \frac {25895367}{128} \, x^{3} - \frac {190742391}{512} \, x^{2} - \frac {48280011}{64} \, x + \frac {9058973 \, {\left (172 \, x - 75\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {84589631}{128} \, \log \left (2 \, x - 1\right ) \]
-54675/56*x^7 - 268515/32*x^6 - 2798631/80*x^5 - 12299769/128*x^4 - 258953 67/128*x^3 - 190742391/512*x^2 - 48280011/64*x + 9058973/2048*(172*x - 75) /(4*x^2 - 4*x + 1) - 84589631/128*log(2*x - 1)
Time = 0.26 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=-\frac {54675}{56} \, x^{7} - \frac {268515}{32} \, x^{6} - \frac {2798631}{80} \, x^{5} - \frac {12299769}{128} \, x^{4} - \frac {25895367}{128} \, x^{3} - \frac {190742391}{512} \, x^{2} - \frac {48280011}{64} \, x + \frac {9058973 \, {\left (172 \, x - 75\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {84589631}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
-54675/56*x^7 - 268515/32*x^6 - 2798631/80*x^5 - 12299769/128*x^4 - 258953 67/128*x^3 - 190742391/512*x^2 - 48280011/64*x + 9058973/2048*(172*x - 75) /(2*x - 1)^2 - 84589631/128*log(abs(2*x - 1))
Time = 1.26 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.70 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx=\frac {\frac {389535839\,x}{2048}-\frac {679422975}{8192}}{x^2-x+\frac {1}{4}}-\frac {84589631\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {48280011\,x}{64}-\frac {190742391\,x^2}{512}-\frac {25895367\,x^3}{128}-\frac {12299769\,x^4}{128}-\frac {2798631\,x^5}{80}-\frac {268515\,x^6}{32}-\frac {54675\,x^7}{56} \]