Integrand size = 22, antiderivative size = 72 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024} \]
[Out]
Time = 0.03 (sec) , antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075 x^9}{2}-\frac {696195 x^8}{32}-\frac {4040847 x^7}{56}-\frac {4736853 x^6}{32}-\frac {34084287 x^5}{160}-\frac {59969727 x^4}{256}-\frac {27480469 x^3}{128}-\frac {94979263 x^2}{512}-\frac {99058879 x}{512}-\frac {99648703 \log (1-2 x)}{1024} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {99058879}{512}-\frac {94979263 x}{256}-\frac {82441407 x^2}{128}-\frac {59969727 x^3}{64}-\frac {34084287 x^4}{32}-\frac {14210559 x^5}{16}-\frac {4040847 x^6}{8}-\frac {696195 x^7}{4}-\frac {54675 x^8}{2}-\frac {99648703}{512 (-1+2 x)}\right ) \, dx \\ & = -\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.04 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=\frac {55685576347}{286720}-\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024} \]
[In]
[Out]
Time = 0.83 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (x -\frac {1}{2}\right )}{1024}\) | \(51\) |
default | \(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\) | \(53\) |
norman | \(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\) | \(53\) |
risch | \(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\) | \(53\) |
meijerg | \(-\frac {99648703 \ln \left (1-2 x \right )}{1024}-7968 x -\frac {12244 x \left (6 x +6\right )}{3}-\frac {7315 x \left (16 x^{2}+12 x +12\right )}{2}-\frac {6741 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{8}-\frac {103509 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{160}-\frac {30267 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{640}-\frac {278721 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{35840}-\frac {891 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{1792}-\frac {1215 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{28672}\) | \(217\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=- \frac {6075 x^{9}}{2} - \frac {696195 x^{8}}{32} - \frac {4040847 x^{7}}{56} - \frac {4736853 x^{6}}{32} - \frac {34084287 x^{5}}{160} - \frac {59969727 x^{4}}{256} - \frac {27480469 x^{3}}{128} - \frac {94979263 x^{2}}{512} - \frac {99058879 x}{512} - \frac {99648703 \log {\left (2 x - 1 \right )}}{1024} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx=-\frac {99058879\,x}{512}-\frac {99648703\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {94979263\,x^2}{512}-\frac {27480469\,x^3}{128}-\frac {59969727\,x^4}{256}-\frac {34084287\,x^5}{160}-\frac {4736853\,x^6}{32}-\frac {4040847\,x^7}{56}-\frac {696195\,x^8}{32}-\frac {6075\,x^9}{2} \]
[In]
[Out]