3.1556 \(\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=69 \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]

[Out]

14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)/64 + (575775*x^4)/16 + (12959
19*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (12386759*Log[1 - 2*x])/128

________________________________________________________________________________________

Rubi [A]  time = 0.0376166, antiderivative size = 69, 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} \[ \frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)/64 + (575775*x^4)/16 + (12959
19*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (12386759*Log[1 - 2*x])/128

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)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{35458963}{256}+\frac{11140101 x}{64}+\frac{11553921 x^2}{64}+\frac{575775 x^3}{4}+\frac{1295919 x^4}{16}+\frac{112995 x^5}{4}+\frac{18225 x^6}{4}+\frac{14235529}{256 (-1+2 x)^2}+\frac{12386759}{64 (-1+2 x)}\right ) \, 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)\\ \end{align*}

Mathematica [A]  time = 0.0206732, size = 64, normalized size = 0.93 \[ \frac{23328000 x^8+157075200 x^7+496202112 x^6+999450144 x^5+1511863920 x^4+2040862320 x^3+3404640680 x^2-6115223546 x+1734146260 (2 x-1) \log (1-2 x)[phone]}{17920 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(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))

________________________________________________________________________________________

Maple [A]  time = 0.006, size = 52, normalized size = 0.8 \begin{align*}{\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 ( 2\,x-1 \right ) }{128}}-{\frac{14235529}{1024\,x-512}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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+12386759/
128*ln(2*x-1)-14235529/512/(2*x-1)

________________________________________________________________________________________

Maxima [A]  time = 1.08793, size = 69, normalized size = 1. \begin{align*} \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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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)

________________________________________________________________________________________

Fricas [A]  time = 1.28208, size = 265, normalized size = 3.84 \begin{align*} \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 )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/17920*(23328000*x^8 + 157075200*x^7 + 496202112*x^6 + 999450144*x^5 + 1511863920*x^4 + 2040862320*x^3 + 3404
640680*x^2 + 1734146260*(2*x - 1)*log(2*x - 1) - 2482127410*x - 498243515)/(2*x - 1)

________________________________________________________________________________________

Sympy [A]  time = 0.112597, size = 61, normalized size = 0.88 \begin{align*} \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} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18225*x**7/28 + 37665*x**6/8 + 1295919*x**5/80 + 575775*x**4/16 + 3851307*x**3/64 + 11140101*x**2/128 + 354589
63*x/256 + 12386759*log(2*x - 1)/128 - 14235529/(1024*x - 512)

________________________________________________________________________________________

Giac [A]  time = 2.06777, size = 126, normalized size = 1.83 \begin{align*} \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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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)