Integrand size = 22, antiderivative size = 69 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {14235529}{512 (1-2 x)}+\frac {35458963 x}{256}+\frac {11140101 x^2}{128}+\frac {3851307 x^3}{64}+\frac {575775 x^4}{16}+\frac {1295919 x^5}{80}+\frac {37665 x^6}{8}+\frac {18225 x^7}{28}+\frac {12386759}{128} \log (1-2 x) \]
14235529/512/(1-2*x)+35458963/256*x+11140101/128*x^2+3851307/64*x^3+575775 /16*x^4+1295919/80*x^5+37665/8*x^6+18225/28*x^7+12386759/128*ln(1-2*x)
Time = 0.02 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.93 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {1318304553-6115223546 x+3404640680 x^2+2040862320 x^3+1511863920 x^4+999450144 x^5+496202112 x^6+157075200 x^7+23328000 x^8+1734146260 (-1+2 x) \log (1-2 x)}{17920 (-1+2 x)} \]
(1318304553 - 6115223546*x + 3404640680*x^2 + 2040862320*x^3 + 1511863920* x^4 + 999450144*x^5 + 496202112*x^6 + 157075200*x^7 + 23328000*x^8 + 17341 46260*(-1 + 2*x)*Log[1 - 2*x])/(17920*(-1 + 2*x))
Time = 0.19 (sec) , antiderivative size = 69, 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.
\(\displaystyle \int \frac {(3 x+2)^6 (5 x+3)^2}{(1-2 x)^2} \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (\frac {18225 x^6}{4}+\frac {112995 x^5}{4}+\frac {1295919 x^4}{16}+\frac {575775 x^3}{4}+\frac {11553921 x^2}{64}+\frac {11140101 x}{64}+\frac {12386759}{64 (2 x-1)}+\frac {14235529}{256 (2 x-1)^2}+\frac {35458963}{256}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {18225 x^7}{28}+\frac {37665 x^6}{8}+\frac {1295919 x^5}{80}+\frac {575775 x^4}{16}+\frac {3851307 x^3}{64}+\frac {11140101 x^2}{128}+\frac {35458963 x}{256}+\frac {14235529}{512 (1-2 x)}+\frac {12386759}{128} \log (1-2 x)\) |
14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (385130 7*x^3)/64 + (575775*x^4)/16 + (1295919*x^5)/80 + (37665*x^6)/8 + (18225*x^ 7)/28 + (12386759*Log[1 - 2*x])/128
3.16.56.3.1 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 = 0.85 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.72
method | result | size |
risch | \(\frac {18225 x^{7}}{28}+\frac {37665 x^{6}}{8}+\frac {1295919 x^{5}}{80}+\frac {575775 x^{4}}{16}+\frac {3851307 x^{3}}{64}+\frac {11140101 x^{2}}{128}+\frac {35458963 x}{256}-\frac {14235529}{1024 \left (x -\frac {1}{2}\right )}+\frac {12386759 \ln \left (-1+2 x \right )}{128}\) | \(50\) |
default | \(\frac {18225 x^{7}}{28}+\frac {37665 x^{6}}{8}+\frac {1295919 x^{5}}{80}+\frac {575775 x^{4}}{16}+\frac {3851307 x^{3}}{64}+\frac {11140101 x^{2}}{128}+\frac {35458963 x}{256}+\frac {12386759 \ln \left (-1+2 x \right )}{128}-\frac {14235529}{512 \left (-1+2 x \right )}\) | \(52\) |
norman | \(\frac {-\frac {12423623}{64} x +\frac {12159431}{64} x^{2}+\frac {3644397}{32} x^{3}+\frac {2699757}{32} x^{4}+\frac {4461831}{80} x^{5}+\frac {553797}{20} x^{6}+\frac {122715}{14} x^{7}+\frac {18225}{14} x^{8}}{-1+2 x}+\frac {12386759 \ln \left (-1+2 x \right )}{128}\) | \(57\) |
parallelrisch | \(\frac {5832000 x^{8}+39268800 x^{7}+124050528 x^{6}+249862536 x^{5}+377965980 x^{4}+510215580 x^{3}+867073130 \ln \left (x -\frac {1}{2}\right ) x +851160170 x^{2}-433536565 \ln \left (x -\frac {1}{2}\right )-869653610 x}{-4480+8960 x}\) | \(62\) |
meijerg | \(\frac {4128 x}{1-2 x}+\frac {12386759 \ln \left (1-2 x \right )}{128}+\frac {9580 x \left (-6 x +6\right )}{3 \left (1-2 x \right )}+\frac {3690 x \left (-8 x^{2}-12 x +12\right )}{1-2 x}+\frac {3789 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{4 \left (1-2 x \right )}+\frac {23337 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{32 \left (1-2 x \right )}+\frac {215541 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{4480 \left (1-2 x \right )}+\frac {3159 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{512 \left (1-2 x \right )}+\frac {405 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{1792 \left (1-2 x \right )}\) | \(230\) |
18225/28*x^7+37665/8*x^6+1295919/80*x^5+575775/16*x^4+3851307/64*x^3+11140 101/128*x^2+35458963/256*x-14235529/1024/(x-1/2)+12386759/128*ln(-1+2*x)
Time = 0.21 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.90 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {23328000 \, x^{8} + 157075200 \, x^{7} + 496202112 \, x^{6} + 999450144 \, x^{5} + 1511863920 \, x^{4} + 2040862320 \, x^{3} + 3404640680 \, x^{2} + 1734146260 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2482127410 \, x - 498243515}{17920 \, {\left (2 \, x - 1\right )}} \]
1/17920*(23328000*x^8 + 157075200*x^7 + 496202112*x^6 + 999450144*x^5 + 15 11863920*x^4 + 2040862320*x^3 + 3404640680*x^2 + 1734146260*(2*x - 1)*log( 2*x - 1) - 2482127410*x - 498243515)/(2*x - 1)
Time = 0.06 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.88 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {18225 x^{7}}{28} + \frac {37665 x^{6}}{8} + \frac {1295919 x^{5}}{80} + \frac {575775 x^{4}}{16} + \frac {3851307 x^{3}}{64} + \frac {11140101 x^{2}}{128} + \frac {35458963 x}{256} + \frac {12386759 \log {\left (2 x - 1 \right )}}{128} - \frac {14235529}{1024 x - 512} \]
18225*x**7/28 + 37665*x**6/8 + 1295919*x**5/80 + 575775*x**4/16 + 3851307* x**3/64 + 11140101*x**2/128 + 35458963*x/256 + 12386759*log(2*x - 1)/128 - 14235529/(1024*x - 512)
Time = 0.19 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {18225}{28} \, x^{7} + \frac {37665}{8} \, x^{6} + \frac {1295919}{80} \, x^{5} + \frac {575775}{16} \, x^{4} + \frac {3851307}{64} \, x^{3} + \frac {11140101}{128} \, x^{2} + \frac {35458963}{256} \, x - \frac {14235529}{512 \, {\left (2 \, x - 1\right )}} + \frac {12386759}{128} \, \log \left (2 \, x - 1\right ) \]
18225/28*x^7 + 37665/8*x^6 + 1295919/80*x^5 + 575775/16*x^4 + 3851307/64*x ^3 + 11140101/128*x^2 + 35458963/256*x - 14235529/512/(2*x - 1) + 12386759 /128*log(2*x - 1)
Time = 0.27 (sec) , antiderivative size = 93, normalized size of antiderivative = 1.35 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {1}{17920} \, {\left (2 \, x - 1\right )}^{7} {\left (\frac {1956150}{2 \, x - 1} + \frac {18894708}{{\left (2 \, x - 1\right )}^{2}} + \frac {108624915}{{\left (2 \, x - 1\right )}^{3}} + \frac {416281950}{{\left (2 \, x - 1\right )}^{4}} + \frac {1148518350}{{\left (2 \, x - 1\right )}^{5}} + \frac {2640379700}{{\left (2 \, x - 1\right )}^{6}} + 91125\right )} - \frac {14235529}{512 \, {\left (2 \, x - 1\right )}} - \frac {12386759}{128} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
1/17920*(2*x - 1)^7*(1956150/(2*x - 1) + 18894708/(2*x - 1)^2 + 108624915/ (2*x - 1)^3 + 416281950/(2*x - 1)^4 + 1148518350/(2*x - 1)^5 + 2640379700/ (2*x - 1)^6 + 91125) - 14235529/512/(2*x - 1) - 12386759/128*log(1/2*abs(2 *x - 1)/(2*x - 1)^2)
Time = 0.06 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.71 \[ \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx=\frac {35458963\,x}{256}+\frac {12386759\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {14235529}{1024\,\left (x-\frac {1}{2}\right )}+\frac {11140101\,x^2}{128}+\frac {3851307\,x^3}{64}+\frac {575775\,x^4}{16}+\frac {1295919\,x^5}{80}+\frac {37665\,x^6}{8}+\frac {18225\,x^7}{28} \]