3.1469 \(\int \frac{(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=72 \[ -\frac{10125 x^9}{2}-\frac{1148175 x^8}{32}-\frac{6596235 x^7}{56}-\frac{7656993 x^6}{32}-\frac{54600291 x^5}{160}-\frac{95317731 x^4}{256}-\frac{130251491 x^3}{384}-\frac{149512931 x^2}{512}-\frac{155706083 x}{512}-\frac{156590819 \log (1-2 x)}{1024} \]

[Out]

(-155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54600291*x^5)/160 - (76
56993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0321318, antiderivative size = 72, 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} \[ -\frac{10125 x^9}{2}-\frac{1148175 x^8}{32}-\frac{6596235 x^7}{56}-\frac{7656993 x^6}{32}-\frac{54600291 x^5}{160}-\frac{95317731 x^4}{256}-\frac{130251491 x^3}{384}-\frac{149512931 x^2}{512}-\frac{155706083 x}{512}-\frac{156590819 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54600291*x^5)/160 - (76
56993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*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} \, dx &=\int \left (-\frac{155706083}{512}-\frac{149512931 x}{256}-\frac{130251491 x^2}{128}-\frac{95317731 x^3}{64}-\frac{54600291 x^4}{32}-\frac{22970979 x^5}{16}-\frac{6596235 x^6}{8}-\frac{1148175 x^7}{4}-\frac{91125 x^8}{2}-\frac{156590819}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac{155706083 x}{512}-\frac{149512931 x^2}{512}-\frac{130251491 x^3}{384}-\frac{95317731 x^4}{256}-\frac{54600291 x^5}{160}-\frac{7656993 x^6}{32}-\frac{6596235 x^7}{56}-\frac{1148175 x^8}{32}-\frac{10125 x^9}{2}-\frac{156590819 \log (1-2 x)}{1024}\\ \end{align*}

Mathematica [A]  time = 0.0141166, size = 75, normalized size = 1.04 \[ -\frac{10125 x^9}{2}-\frac{1148175 x^8}{32}-\frac{6596235 x^7}{56}-\frac{7656993 x^6}{32}-\frac{54600291 x^5}{160}-\frac{95317731 x^4}{256}-\frac{130251491 x^3}{384}-\frac{149512931 x^2}{512}-\frac{155706083 x}{512}-\frac{156590819 \log (1-2 x)}{1024}+\frac{263385079253}{860160} \]

Antiderivative was successfully verified.

[In]

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

[Out]

263385079253/860160 - (155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54
600291*x^5)/160 - (7656993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*Log[1 -
2*x])/1024

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Maple [A]  time = 0.004, size = 53, normalized size = 0.7 \begin{align*} -{\frac{10125\,{x}^{9}}{2}}-{\frac{1148175\,{x}^{8}}{32}}-{\frac{6596235\,{x}^{7}}{56}}-{\frac{7656993\,{x}^{6}}{32}}-{\frac{54600291\,{x}^{5}}{160}}-{\frac{95317731\,{x}^{4}}{256}}-{\frac{130251491\,{x}^{3}}{384}}-{\frac{149512931\,{x}^{2}}{512}}-{\frac{155706083\,x}{512}}-{\frac{156590819\,\ln \left ( 2\,x-1 \right ) }{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),x)

[Out]

-10125/2*x^9-1148175/32*x^8-6596235/56*x^7-7656993/32*x^6-54600291/160*x^5-95317731/256*x^4-130251491/384*x^3-
149512931/512*x^2-155706083/512*x-156590819/1024*ln(2*x-1)

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Maxima [A]  time = 1.07733, size = 70, normalized size = 0.97 \begin{align*} -\frac{10125}{2} \, x^{9} - \frac{1148175}{32} \, x^{8} - \frac{6596235}{56} \, x^{7} - \frac{7656993}{32} \, x^{6} - \frac{54600291}{160} \, x^{5} - \frac{95317731}{256} \, x^{4} - \frac{130251491}{384} \, x^{3} - \frac{149512931}{512} \, x^{2} - \frac{155706083}{512} \, x - \frac{156590819}{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),x, algorithm="maxima")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(2*x - 1)

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Fricas [A]  time = 1.40899, size = 258, normalized size = 3.58 \begin{align*} -\frac{10125}{2} \, x^{9} - \frac{1148175}{32} \, x^{8} - \frac{6596235}{56} \, x^{7} - \frac{7656993}{32} \, x^{6} - \frac{54600291}{160} \, x^{5} - \frac{95317731}{256} \, x^{4} - \frac{130251491}{384} \, x^{3} - \frac{149512931}{512} \, x^{2} - \frac{155706083}{512} \, x - \frac{156590819}{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),x, algorithm="fricas")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(2*x - 1)

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Sympy [A]  time = 0.108565, size = 70, normalized size = 0.97 \begin{align*} - \frac{10125 x^{9}}{2} - \frac{1148175 x^{8}}{32} - \frac{6596235 x^{7}}{56} - \frac{7656993 x^{6}}{32} - \frac{54600291 x^{5}}{160} - \frac{95317731 x^{4}}{256} - \frac{130251491 x^{3}}{384} - \frac{149512931 x^{2}}{512} - \frac{155706083 x}{512} - \frac{156590819 \log{\left (2 x - 1 \right )}}{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),x)

[Out]

-10125*x**9/2 - 1148175*x**8/32 - 6596235*x**7/56 - 7656993*x**6/32 - 54600291*x**5/160 - 95317731*x**4/256 -
130251491*x**3/384 - 149512931*x**2/512 - 155706083*x/512 - 156590819*log(2*x - 1)/1024

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Giac [A]  time = 1.2492, size = 72, normalized size = 1. \begin{align*} -\frac{10125}{2} \, x^{9} - \frac{1148175}{32} \, x^{8} - \frac{6596235}{56} \, x^{7} - \frac{7656993}{32} \, x^{6} - \frac{54600291}{160} \, x^{5} - \frac{95317731}{256} \, x^{4} - \frac{130251491}{384} \, x^{3} - \frac{149512931}{512} \, x^{2} - \frac{155706083}{512} \, x - \frac{156590819}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\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),x, algorithm="giac")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(abs(2*x - 1))