Integrand size = 22, antiderivative size = 79 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=-\frac {695181625 x}{1024}-\frac {677093689 x^2}{1024}-\frac {204901139 x^3}{256}-\frac {487203129 x^4}{512}-\frac {316246329 x^5}{320}-\frac {53031699 x^6}{64}-\frac {8399295 x^7}{16}-\frac {14907321 x^8}{64}-\frac {256365 x^9}{4}-\frac {32805 x^{10}}{4}-\frac {697540921 \log (1-2 x)}{2048} \]
-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-487203129/512*x^4-3 16246329/320*x^5-53031699/64*x^6-8399295/16*x^7-14907321/64*x^8-256365/4*x ^9-32805/4*x^10-697540921/2048*ln(1-2*x)
Time = 0.01 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.78 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=\frac {58429239347-55614530000 x-54167495120 x^2-65568364480 x^3-77952500640 x^4-80959060224 x^5-67880574720 x^6-43004390400 x^7-19081370880 x^8-5250355200 x^9-671846400 x^{10}-27901636840 \log (1-2 x)}{81920} \]
(58429239347 - 55614530000*x - 54167495120*x^2 - 65568364480*x^3 - 7795250 0640*x^4 - 80959060224*x^5 - 67880574720*x^6 - 43004390400*x^7 - 190813708 80*x^8 - 5250355200*x^9 - 671846400*x^10 - 27901636840*Log[1 - 2*x])/81920
Time = 0.19 (sec) , antiderivative size = 79, 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.
| \(\displaystyle \int \frac {(3 x+2)^8 (5 x+3)^2}{1-2 x} \, dx\) |
| \(\Big \downarrow \) 99 |
| \(\displaystyle \int \left (-\frac {164025 x^9}{2}-\frac {2307285 x^8}{4}-\frac {14907321 x^7}{8}-\frac {58795065 x^6}{16}-\frac {159095097 x^5}{32}-\frac {316246329 x^4}{64}-\frac {487203129 x^3}{128}-\frac {614703417 x^2}{256}-\frac {677093689 x}{512}-\frac {697540921}{1024 (2 x-1)}-\frac {695181625}{1024}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {32805 x^{10}}{4}-\frac {256365 x^9}{4}-\frac {14907321 x^8}{64}-\frac {8399295 x^7}{16}-\frac {53031699 x^6}{64}-\frac {316246329 x^5}{320}-\frac {487203129 x^4}{512}-\frac {204901139 x^3}{256}-\frac {677093689 x^2}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \log (1-2 x)}{2048}\) |
(-695181625*x)/1024 - (677093689*x^2)/1024 - (204901139*x^3)/256 - (487203 129*x^4)/512 - (316246329*x^5)/320 - (53031699*x^6)/64 - (8399295*x^7)/16 - (14907321*x^8)/64 - (256365*x^9)/4 - (32805*x^10)/4 - (697540921*Log[1 - 2*x])/2048
3.15.51.3.1 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 = 2.56 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.71
| method | result | size |
| parallelrisch | \(-\frac {32805 x^{10}}{4}-\frac {256365 x^{9}}{4}-\frac {14907321 x^{8}}{64}-\frac {8399295 x^{7}}{16}-\frac {53031699 x^{6}}{64}-\frac {316246329 x^{5}}{320}-\frac {487203129 x^{4}}{512}-\frac {204901139 x^{3}}{256}-\frac {677093689 x^{2}}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \ln \left (x -\frac {1}{2}\right )}{2048}\) | \(56\) |
| default | \(-\frac {32805 x^{10}}{4}-\frac {256365 x^{9}}{4}-\frac {14907321 x^{8}}{64}-\frac {8399295 x^{7}}{16}-\frac {53031699 x^{6}}{64}-\frac {316246329 x^{5}}{320}-\frac {487203129 x^{4}}{512}-\frac {204901139 x^{3}}{256}-\frac {677093689 x^{2}}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
| norman | \(-\frac {32805 x^{10}}{4}-\frac {256365 x^{9}}{4}-\frac {14907321 x^{8}}{64}-\frac {8399295 x^{7}}{16}-\frac {53031699 x^{6}}{64}-\frac {316246329 x^{5}}{320}-\frac {487203129 x^{4}}{512}-\frac {204901139 x^{3}}{256}-\frac {677093689 x^{2}}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
| risch | \(-\frac {32805 x^{10}}{4}-\frac {256365 x^{9}}{4}-\frac {14907321 x^{8}}{64}-\frac {8399295 x^{7}}{16}-\frac {53031699 x^{6}}{64}-\frac {316246329 x^{5}}{320}-\frac {487203129 x^{4}}{512}-\frac {204901139 x^{3}}{256}-\frac {677093689 x^{2}}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
| meijerg | \(-\frac {697540921 \ln \left (1-2 x \right )}{2048}-\frac {114291 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{2240}-\frac {350001 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{71680}-\frac {30464 x \left (6 x +6\right )}{3}-10376 x \left (16 x^{2}+12 x +12\right )-\frac {1701 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{2048}-\frac {3645 x \left (1419264 x^{9}+788480 x^{8}+443520 x^{7}+253440 x^{6}+147840 x^{5}+88704 x^{4}+55440 x^{3}+36960 x^{2}+27720 x +27720\right )}{630784}-17664 x -\frac {12789 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{5}-\frac {18657 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{80}-\frac {5565 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{2}\) | \(265\) |
-32805/4*x^10-256365/4*x^9-14907321/64*x^8-8399295/16*x^7-53031699/64*x^6- 316246329/320*x^5-487203129/512*x^4-204901139/256*x^3-677093689/1024*x^2-6 95181625/1024*x-697540921/2048*ln(x-1/2)
Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=-\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left (2 \, x - 1\right ) \]
-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699 /64*x^6 - 316246329/320*x^5 - 487203129/512*x^4 - 204901139/256*x^3 - 6770 93689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(2*x - 1)
Time = 0.05 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=- \frac {32805 x^{10}}{4} - \frac {256365 x^{9}}{4} - \frac {14907321 x^{8}}{64} - \frac {8399295 x^{7}}{16} - \frac {53031699 x^{6}}{64} - \frac {316246329 x^{5}}{320} - \frac {487203129 x^{4}}{512} - \frac {204901139 x^{3}}{256} - \frac {677093689 x^{2}}{1024} - \frac {695181625 x}{1024} - \frac {697540921 \log {\left (2 x - 1 \right )}}{2048} \]
-32805*x**10/4 - 256365*x**9/4 - 14907321*x**8/64 - 8399295*x**7/16 - 5303 1699*x**6/64 - 316246329*x**5/320 - 487203129*x**4/512 - 204901139*x**3/25 6 - 677093689*x**2/1024 - 695181625*x/1024 - 697540921*log(2*x - 1)/2048
Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=-\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left (2 \, x - 1\right ) \]
-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699 /64*x^6 - 316246329/320*x^5 - 487203129/512*x^4 - 204901139/256*x^3 - 6770 93689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(2*x - 1)
Time = 0.30 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=-\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699 /64*x^6 - 316246329/320*x^5 - 487203129/512*x^4 - 204901139/256*x^3 - 6770 93689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(abs(2*x - 1))
Time = 0.06 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.70 \[ \int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx=-\frac {695181625\,x}{1024}-\frac {697540921\,\ln \left (x-\frac {1}{2}\right )}{2048}-\frac {677093689\,x^2}{1024}-\frac {204901139\,x^3}{256}-\frac {487203129\,x^4}{512}-\frac {316246329\,x^5}{320}-\frac {53031699\,x^6}{64}-\frac {8399295\,x^7}{16}-\frac {14907321\,x^8}{64}-\frac {256365\,x^9}{4}-\frac {32805\,x^{10}}{4} \]