3.1452 \(\int \frac{(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=72 \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024} \]

[Out]

(-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (34084287*x^5)/160 - (47368
53*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0350201, 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} \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (34084287*x^5)/160 - (47368
53*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*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)^7 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac{99058879}{512}-\frac{94979263 x}{256}-\frac{82441407 x^2}{128}-\frac{59969727 x^3}{64}-\frac{34084287 x^4}{32}-\frac{14210559 x^5}{16}-\frac{4040847 x^6}{8}-\frac{696195 x^7}{4}-\frac{54675 x^8}{2}-\frac{99648703}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac{99058879 x}{512}-\frac{94979263 x^2}{512}-\frac{27480469 x^3}{128}-\frac{59969727 x^4}{256}-\frac{34084287 x^5}{160}-\frac{4736853 x^6}{32}-\frac{4040847 x^7}{56}-\frac{696195 x^8}{32}-\frac{6075 x^9}{2}-\frac{99648703 \log (1-2 x)}{1024}\\ \end{align*}

Mathematica [A]  time = 0.0136671, size = 75, normalized size = 1.04 \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024}+\frac{55685576347}{286720} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

55685576347/286720 - (99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (340842
87*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*Log[1 - 2*x])/1
024

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Maple [A]  time = 0.002, size = 53, normalized size = 0.7 \begin{align*} -{\frac{6075\,{x}^{9}}{2}}-{\frac{696195\,{x}^{8}}{32}}-{\frac{4040847\,{x}^{7}}{56}}-{\frac{4736853\,{x}^{6}}{32}}-{\frac{34084287\,{x}^{5}}{160}}-{\frac{59969727\,{x}^{4}}{256}}-{\frac{27480469\,{x}^{3}}{128}}-{\frac{94979263\,{x}^{2}}{512}}-{\frac{99058879\,x}{512}}-{\frac{99648703\,\ln \left ( 2\,x-1 \right ) }{1024}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^7*(3+5*x)^2/(1-2*x),x)

[Out]

-6075/2*x^9-696195/32*x^8-4040847/56*x^7-4736853/32*x^6-34084287/160*x^5-59969727/256*x^4-27480469/128*x^3-949
79263/512*x^2-99058879/512*x-99648703/1024*ln(2*x-1)

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Maxima [A]  time = 1.033, size = 70, normalized size = 0.97 \begin{align*} -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm="maxima")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(2*x - 1)

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Fricas [A]  time = 1.51209, size = 250, normalized size = 3.47 \begin{align*} -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm="fricas")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(2*x - 1)

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Sympy [A]  time = 0.109433, size = 70, normalized size = 0.97 \begin{align*} - \frac{6075 x^{9}}{2} - \frac{696195 x^{8}}{32} - \frac{4040847 x^{7}}{56} - \frac{4736853 x^{6}}{32} - \frac{34084287 x^{5}}{160} - \frac{59969727 x^{4}}{256} - \frac{27480469 x^{3}}{128} - \frac{94979263 x^{2}}{512} - \frac{99058879 x}{512} - \frac{99648703 \log{\left (2 x - 1 \right )}}{1024} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**7*(3+5*x)**2/(1-2*x),x)

[Out]

-6075*x**9/2 - 696195*x**8/32 - 4040847*x**7/56 - 4736853*x**6/32 - 34084287*x**5/160 - 59969727*x**4/256 - 27
480469*x**3/128 - 94979263*x**2/512 - 99058879*x/512 - 99648703*log(2*x - 1)/1024

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Giac [A]  time = 1.22617, size = 72, normalized size = 1. \begin{align*} -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{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)^7*(3+5*x)^2/(1-2*x),x, algorithm="giac")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(abs(2*x - 1))