3.1573 \(\int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=76 \[ \frac{91125 x^8}{32}+\frac{309825 x^7}{14}+\frac{2611845 x^6}{32}+\frac{15403257 x^5}{80}+\frac{85406805 x^4}{256}+\frac{7530189 x^3}{16}+\frac{310976027 x^2}{512}+\frac{230244479 x}{256}+\frac{156590819}{1024 (1-2 x)}+\frac{616195041 \log (1-2 x)}{1024} \]

[Out]

156590819/(1024*(1 - 2*x)) + (230244479*x)/256 + (310976027*x^2)/512 + (7530189*x^3)/16 + (85406805*x^4)/256 +
(15403257*x^5)/80 + (2611845*x^6)/32 + (309825*x^7)/14 + (91125*x^8)/32 + (616195041*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0414432, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{91125 x^8}{32}+\frac{309825 x^7}{14}+\frac{2611845 x^6}{32}+\frac{15403257 x^5}{80}+\frac{85406805 x^4}{256}+\frac{7530189 x^3}{16}+\frac{310976027 x^2}{512}+\frac{230244479 x}{256}+\frac{156590819}{1024 (1-2 x)}+\frac{616195041 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

156590819/(1024*(1 - 2*x)) + (230244479*x)/256 + (310976027*x^2)/512 + (7530189*x^3)/16 + (85406805*x^4)/256 +
(15403257*x^5)/80 + (2611845*x^6)/32 + (309825*x^7)/14 + (91125*x^8)/32 + (616195041*Log[1 - 2*x])/1024

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(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]))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{230244479}{256}+\frac{310976027 x}{256}+\frac{22590567 x^2}{16}+\frac{85406805 x^3}{64}+\frac{15403257 x^4}{16}+\frac{7835535 x^5}{16}+\frac{309825 x^6}{2}+\frac{91125 x^7}{4}+\frac{156590819}{512 (-1+2 x)^2}+\frac{616195041}{512 (-1+2 x)}\right ) \, dx\\ &=\frac{156590819}{1024 (1-2 x)}+\frac{230244479 x}{256}+\frac{310976027 x^2}{512}+\frac{7530189 x^3}{16}+\frac{85406805 x^4}{256}+\frac{15403257 x^5}{80}+\frac{2611845 x^6}{32}+\frac{309825 x^7}{14}+\frac{91125 x^8}{32}+\frac{616195041 \log (1-2 x)}{1024}\\ \end{align*}

Mathematica [A]  time = 0.0173286, size = 69, normalized size = 0.91 \[ \frac{1632960000 x^9+11873952000 x^8+40459046400 x^7+87008414976 x^6+136105970112 x^5+174226352160 x^4+213352163360 x^3+341601057840 x^2-652800288858 x+172534611480 (2 x-1) \log (1-2 x)[phone]}{286720 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

(153617806869 - 652800288858*x + 341601057840*x^2 + 213352163360*x^3 + 174226352160*x^4 + 136105970112*x^5 + 8
7008414976*x^6 + 40459046400*x^7 + 11873952000*x^8 + 1632960000*x^9 + 172534611480*(-1 + 2*x)*Log[1 - 2*x])/(2
86720*(-1 + 2*x))

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Maple [A]  time = 0.004, size = 57, normalized size = 0.8 \begin{align*}{\frac{91125\,{x}^{8}}{32}}+{\frac{309825\,{x}^{7}}{14}}+{\frac{2611845\,{x}^{6}}{32}}+{\frac{15403257\,{x}^{5}}{80}}+{\frac{85406805\,{x}^{4}}{256}}+{\frac{7530189\,{x}^{3}}{16}}+{\frac{310976027\,{x}^{2}}{512}}+{\frac{230244479\,x}{256}}+{\frac{616195041\,\ln \left ( 2\,x-1 \right ) }{1024}}-{\frac{156590819}{2048\,x-1024}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x)

[Out]

91125/32*x^8+309825/14*x^7+2611845/32*x^6+15403257/80*x^5+85406805/256*x^4+7530189/16*x^3+310976027/512*x^2+23
0244479/256*x+616195041/1024*ln(2*x-1)-156590819/1024/(2*x-1)

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Maxima [A]  time = 1.03738, size = 76, normalized size = 1. \begin{align*} \frac{91125}{32} \, x^{8} + \frac{309825}{14} \, x^{7} + \frac{2611845}{32} \, x^{6} + \frac{15403257}{80} \, x^{5} + \frac{85406805}{256} \, x^{4} + \frac{7530189}{16} \, x^{3} + \frac{310976027}{512} \, x^{2} + \frac{230244479}{256} \, x - \frac{156590819}{1024 \,{\left (2 \, x - 1\right )}} + \frac{616195041}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x, algorithm="maxima")

[Out]

91125/32*x^8 + 309825/14*x^7 + 2611845/32*x^6 + 15403257/80*x^5 + 85406805/256*x^4 + 7530189/16*x^3 + 31097602
7/512*x^2 + 230244479/256*x - 156590819/1024/(2*x - 1) + 616195041/1024*log(2*x - 1)

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Fricas [A]  time = 1.33072, size = 304, normalized size = 4. \begin{align*} \frac{204120000 \, x^{9} + 1484244000 \, x^{8} + 5057380800 \, x^{7} + 10876051872 \, x^{6} + 17013246264 \, x^{5} + 21778294020 \, x^{4} + 26669020420 \, x^{3} + 42700132230 \, x^{2} + 21566826435 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 32234227060 \, x - 5480678665}{35840 \,{\left (2 \, x - 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/35840*(204120000*x^9 + 1484244000*x^8 + 5057380800*x^7 + 10876051872*x^6 + 17013246264*x^5 + 21778294020*x^4
+ 26669020420*x^3 + 42700132230*x^2 + 21566826435*(2*x - 1)*log(2*x - 1) - 32234227060*x - 5480678665)/(2*x -
1)

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Sympy [A]  time = 0.126978, size = 68, normalized size = 0.89 \begin{align*} \frac{91125 x^{8}}{32} + \frac{309825 x^{7}}{14} + \frac{2611845 x^{6}}{32} + \frac{15403257 x^{5}}{80} + \frac{85406805 x^{4}}{256} + \frac{7530189 x^{3}}{16} + \frac{310976027 x^{2}}{512} + \frac{230244479 x}{256} + \frac{616195041 \log{\left (2 x - 1 \right )}}{1024} - \frac{156590819}{2048 x - 1024} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**6*(3+5*x)**3/(1-2*x)**2,x)

[Out]

91125*x**8/32 + 309825*x**7/14 + 2611845*x**6/32 + 15403257*x**5/80 + 85406805*x**4/256 + 7530189*x**3/16 + 31
0976027*x**2/512 + 230244479*x/256 + 616195041*log(2*x - 1)/1024 - 156590819/(2048*x - 1024)

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Giac [A]  time = 2.4547, size = 138, normalized size = 1.82 \begin{align*} \frac{1}{286720} \,{\left (2 \, x - 1\right )}^{8}{\left (\frac{75087000}{2 \, x - 1} + \frac{801964800}{{\left (2 \, x - 1\right )}^{2}} + \frac{5138731584}{{\left (2 \, x - 1\right )}^{3}} + \frac{22047451020}{{\left (2 \, x - 1\right )}^{4}} + \frac{67259967600}{{\left (2 \, x - 1\right )}^{5}} + \frac{153877208800}{{\left (2 \, x - 1\right )}^{6}} + \frac{301719264000}{{\left (2 \, x - 1\right )}^{7}} + 3189375\right )} - \frac{156590819}{1024 \,{\left (2 \, x - 1\right )}} - \frac{616195041}{1024} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/286720*(2*x - 1)^8*(75087000/(2*x - 1) + 801964800/(2*x - 1)^2 + 5138731584/(2*x - 1)^3 + 22047451020/(2*x -
1)^4 + 67259967600/(2*x - 1)^5 + 153877208800/(2*x - 1)^6 + 301719264000/(2*x - 1)^7 + 3189375) - 156590819/1
024/(2*x - 1) - 616195041/1024*log(1/2*abs(2*x - 1)/(2*x - 1)^2)