Integrand size = 22, antiderivative size = 80 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=\frac {156590819}{2048 (1-2 x)^2}-\frac {616195041}{1024 (1-2 x)}-\frac {308539921 x}{256}-\frac {306103815 x^2}{512}-\frac {41793093 x^3}{128}-\frac {19986237 x^4}{128}-\frac {229149 x^5}{4}-\frac {443475 x^6}{32}-\frac {91125 x^7}{56}-\frac {33674025}{32} \log (1-2 x) \]
156590819/2048/(1-2*x)^2-616195041/1024/(1-2*x)-308539921/256*x-306103815/ 512*x^2-41793093/128*x^3-19986237/128*x^4-229149/4*x^5-443475/32*x^6-91125 /56*x^7-33674025/32*ln(1-2*x)
Time = 0.02 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=-\frac {-1001301969+11541996324 x-26671311588 x^2+9877535360 x^3+4449695040 x^4+2647685376 x^5+1466857728 x^6+628425216 x^7+175348800 x^8+23328000 x^9+3771490800 (1-2 x)^2 \log (1-2 x)}{3584 (1-2 x)^2} \]
-1/3584*(-1001301969 + 11541996324*x - 26671311588*x^2 + 9877535360*x^3 + 4449695040*x^4 + 2647685376*x^5 + 1466857728*x^6 + 628425216*x^7 + 1753488 00*x^8 + 23328000*x^9 + 3771490800*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2
Time = 0.20 (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.
\(\displaystyle \int \frac {(3 x+2)^6 (5 x+3)^3}{(1-2 x)^3} \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (-\frac {91125 x^6}{8}-\frac {1330425 x^5}{16}-\frac {1145745 x^4}{4}-\frac {19986237 x^3}{32}-\frac {125379279 x^2}{128}-\frac {306103815 x}{256}-\frac {33674025}{16 (2 x-1)}-\frac {616195041}{512 (2 x-1)^2}-\frac {156590819}{512 (2 x-1)^3}-\frac {308539921}{256}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -\frac {91125 x^7}{56}-\frac {443475 x^6}{32}-\frac {229149 x^5}{4}-\frac {19986237 x^4}{128}-\frac {41793093 x^3}{128}-\frac {306103815 x^2}{512}-\frac {308539921 x}{256}-\frac {616195041}{1024 (1-2 x)}+\frac {156590819}{2048 (1-2 x)^2}-\frac {33674025}{32} \log (1-2 x)\) |
156590819/(2048*(1 - 2*x)^2) - 616195041/(1024*(1 - 2*x)) - (308539921*x)/ 256 - (306103815*x^2)/512 - (41793093*x^3)/128 - (19986237*x^4)/128 - (229 149*x^5)/4 - (443475*x^6)/32 - (91125*x^7)/56 - (33674025*Log[1 - 2*x])/32
3.17.59.3.1 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 = 0.89 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}+\frac {\frac {616195041 x}{512}-\frac {1075799263}{2048}}{\left (-1+2 x \right )^{2}}-\frac {33674025 \ln \left (-1+2 x \right )}{32}\) | \(57\) |
default | \(-\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}-\frac {33674025 \ln \left (-1+2 x \right )}{32}+\frac {616195041}{1024 \left (-1+2 x \right )}+\frac {156590819}{2048 \left (-1+2 x \right )^{2}}\) | \(61\) |
norman | \(\frac {-\frac {33646377}{16} x +\frac {101187963}{16} x^{2}-\frac {11024035}{4} x^{3}-\frac {9932355}{8} x^{4}-\frac {1477503}{2} x^{5}-\frac {818559}{2} x^{6}-\frac {1227393}{7} x^{7}-\frac {2739825}{56} x^{8}-\frac {91125}{14} x^{9}}{\left (-1+2 x \right )^{2}}-\frac {33674025 \ln \left (-1+2 x \right )}{32}\) | \(62\) |
parallelrisch | \(-\frac {1458000 x^{9}+10959300 x^{8}+39276576 x^{7}+91678608 x^{6}+165480336 x^{5}+278105940 x^{4}+942872700 \ln \left (x -\frac {1}{2}\right ) x^{2}+617345960 x^{3}-942872700 \ln \left (x -\frac {1}{2}\right ) x -1416631482 x^{2}+235718175 \ln \left (x -\frac {1}{2}\right )+471049278 x}{224 \left (-1+2 x \right )^{2}}\) | \(76\) |
meijerg | \(\frac {864 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}-\frac {272403 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{1024 \left (1-2 x \right )^{2}}-\frac {33674025 \ln \left (1-2 x \right )}{32}-\frac {11745 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{512 \left (1-2 x \right )^{2}}-\frac {18225 x \left (2560 x^{8}+1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{7168 \left (1-2 x \right )^{2}}-\frac {34115 x \left (16 x^{2}-36 x +12\right )}{2 \left (1-2 x \right )^{2}}-\frac {63621 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{8 \left (1-2 x \right )^{2}}-\frac {6270 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}-\frac {10296 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{\left (1-2 x \right )^{2}}-\frac {2046843 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}+\frac {12096 x^{2}}{\left (1-2 x \right )^{2}}\) | \(297\) |
-91125/56*x^7-443475/32*x^6-229149/4*x^5-19986237/128*x^4-41793093/128*x^3 -306103815/512*x^2-308539921/256*x+4*(616195041/2048*x-1075799263/8192)/(- 1+2*x)^2-33674025/32*ln(-1+2*x)
Time = 0.22 (sec) , antiderivative size = 77, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=-\frac {93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 24774428 \, x + 7530594841}{14336 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
-1/14336*(93312000*x^9 + 701395200*x^8 + 2513700864*x^7 + 5867430912*x^6 + 10590741504*x^5 + 17798780160*x^4 + 39510141440*x^3 - 60542035484*x^2 + 1 5085963200*(4*x^2 - 4*x + 1)*log(2*x - 1) + 24774428*x + 7530594841)/(4*x^ 2 - 4*x + 1)
Time = 0.07 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=- \frac {91125 x^{7}}{56} - \frac {443475 x^{6}}{32} - \frac {229149 x^{5}}{4} - \frac {19986237 x^{4}}{128} - \frac {41793093 x^{3}}{128} - \frac {306103815 x^{2}}{512} - \frac {308539921 x}{256} - \frac {1075799263 - 2464780164 x}{8192 x^{2} - 8192 x + 2048} - \frac {33674025 \log {\left (2 x - 1 \right )}}{32} \]
-91125*x**7/56 - 443475*x**6/32 - 229149*x**5/4 - 19986237*x**4/128 - 4179 3093*x**3/128 - 306103815*x**2/512 - 308539921*x/256 - (1075799263 - 24647 80164*x)/(8192*x**2 - 8192*x + 2048) - 33674025*log(2*x - 1)/32
Time = 0.19 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.76 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=-\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {33674025}{32} \, \log \left (2 \, x - 1\right ) \]
-91125/56*x^7 - 443475/32*x^6 - 229149/4*x^5 - 19986237/128*x^4 - 41793093 /128*x^3 - 306103815/512*x^2 - 308539921/256*x + 2033647/2048*(1212*x - 52 9)/(4*x^2 - 4*x + 1) - 33674025/32*log(2*x - 1)
Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=-\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {33674025}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
-91125/56*x^7 - 443475/32*x^6 - 229149/4*x^5 - 19986237/128*x^4 - 41793093 /128*x^3 - 306103815/512*x^2 - 308539921/256*x + 2033647/2048*(1212*x - 52 9)/(2*x - 1)^2 - 33674025/32*log(abs(2*x - 1))
Time = 1.24 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.70 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx=\frac {\frac {616195041\,x}{2048}-\frac {1075799263}{8192}}{x^2-x+\frac {1}{4}}-\frac {33674025\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {308539921\,x}{256}-\frac {306103815\,x^2}{512}-\frac {41793093\,x^3}{128}-\frac {19986237\,x^4}{128}-\frac {229149\,x^5}{4}-\frac {443475\,x^6}{32}-\frac {91125\,x^7}{56} \]