3.1451 \(\int \frac {(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=79 \[ -\frac {32805 x^{10}}{4}-\frac {256365 x^9}{4}-\frac {14907321 x^8}{64}-\frac {8399295 x^7}{16}-\frac {53031699 x^6}{64}-\frac {316246329 x^5}{320}-\frac {487203129 x^4}{512}-\frac {204901139 x^3}{256}-\frac {677093689 x^2}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \log (1-2 x)}{2048} \]

[Out]

-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-487203129/512*x^4-316246329/320*x^5-53031699/64*x^6-839
9295/16*x^7-14907321/64*x^8-256365/4*x^9-32805/4*x^10-697540921/2048*ln(1-2*x)

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Rubi [A]  time = 0.04, antiderivative size = 79, normalized size of antiderivative = 1.00, 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} \[ -\frac {32805 x^{10}}{4}-\frac {256365 x^9}{4}-\frac {14907321 x^8}{64}-\frac {8399295 x^7}{16}-\frac {53031699 x^6}{64}-\frac {316246329 x^5}{320}-\frac {487203129 x^4}{512}-\frac {204901139 x^3}{256}-\frac {677093689 x^2}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \log (1-2 x)}{2048} \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(-695181625*x)/1024 - (677093689*x^2)/1024 - (204901139*x^3)/256 - (487203129*x^4)/512 - (316246329*x^5)/320 -
(53031699*x^6)/64 - (8399295*x^7)/16 - (14907321*x^8)/64 - (256365*x^9)/4 - (32805*x^10)/4 - (697540921*Log[1
- 2*x])/2048

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)^8 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {695181625}{1024}-\frac {677093689 x}{512}-\frac {614703417 x^2}{256}-\frac {487203129 x^3}{128}-\frac {316246329 x^4}{64}-\frac {159095097 x^5}{32}-\frac {58795065 x^6}{16}-\frac {14907321 x^7}{8}-\frac {2307285 x^8}{4}-\frac {164025 x^9}{2}-\frac {697540921}{1024 (-1+2 x)}\right ) \, dx\\ &=-\frac {695181625 x}{1024}-\frac {677093689 x^2}{1024}-\frac {204901139 x^3}{256}-\frac {487203129 x^4}{512}-\frac {316246329 x^5}{320}-\frac {53031699 x^6}{64}-\frac {8399295 x^7}{16}-\frac {14907321 x^8}{64}-\frac {256365 x^9}{4}-\frac {32805 x^{10}}{4}-\frac {697540921 \log (1-2 x)}{2048}\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 62, normalized size = 0.78 \[ \frac {-671846400 x^{10}-5250355200 x^9-19081370880 x^8-43004390400 x^7-67880574720 x^6-80959060224 x^5-77952500640 x^4-65568364480 x^3-54167495120 x^2-55614530000 x-27901636840 \log (1-2 x)[phone]}{81920} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(58429239347 - 55614530000*x - 54167495120*x^2 - 65568364480*x^3 - 77952500640*x^4 - 80959060224*x^5 - 6788057
4720*x^6 - 43004390400*x^7 - 19081370880*x^8 - 5250355200*x^9 - 671846400*x^10 - 27901636840*Log[1 - 2*x])/819
20

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fricas [A]  time = 0.85, size = 57, normalized size = 0.72 \[ -\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^8*(3+5*x)^2/(1-2*x),x, algorithm="fricas")

[Out]

-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699/64*x^6 - 316246329/320*x^5 - 487203
129/512*x^4 - 204901139/256*x^3 - 677093689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(2*x - 1)

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giac [A]  time = 0.93, size = 58, normalized size = 0.73 \[ -\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^8*(3+5*x)^2/(1-2*x),x, algorithm="giac")

[Out]

-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699/64*x^6 - 316246329/320*x^5 - 487203
129/512*x^4 - 204901139/256*x^3 - 677093689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(abs(2*x - 1))

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maple [A]  time = 0.00, size = 58, normalized size = 0.73 \[ -\frac {32805 x^{10}}{4}-\frac {256365 x^{9}}{4}-\frac {14907321 x^{8}}{64}-\frac {8399295 x^{7}}{16}-\frac {53031699 x^{6}}{64}-\frac {316246329 x^{5}}{320}-\frac {487203129 x^{4}}{512}-\frac {204901139 x^{3}}{256}-\frac {677093689 x^{2}}{1024}-\frac {695181625 x}{1024}-\frac {697540921 \ln \left (2 x -1\right )}{2048} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^8*(5*x+3)^2/(1-2*x),x)

[Out]

-32805/4*x^10-256365/4*x^9-14907321/64*x^8-8399295/16*x^7-53031699/64*x^6-316246329/320*x^5-487203129/512*x^4-
204901139/256*x^3-677093689/1024*x^2-695181625/1024*x-697540921/2048*ln(2*x-1)

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maxima [A]  time = 0.57, size = 57, normalized size = 0.72 \[ -\frac {32805}{4} \, x^{10} - \frac {256365}{4} \, x^{9} - \frac {14907321}{64} \, x^{8} - \frac {8399295}{16} \, x^{7} - \frac {53031699}{64} \, x^{6} - \frac {316246329}{320} \, x^{5} - \frac {487203129}{512} \, x^{4} - \frac {204901139}{256} \, x^{3} - \frac {677093689}{1024} \, x^{2} - \frac {695181625}{1024} \, x - \frac {697540921}{2048} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^8*(3+5*x)^2/(1-2*x),x, algorithm="maxima")

[Out]

-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699/64*x^6 - 316246329/320*x^5 - 487203
129/512*x^4 - 204901139/256*x^3 - 677093689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(2*x - 1)

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mupad [B]  time = 0.06, size = 55, normalized size = 0.70 \[ -\frac {695181625\,x}{1024}-\frac {697540921\,\ln \left (x-\frac {1}{2}\right )}{2048}-\frac {677093689\,x^2}{1024}-\frac {204901139\,x^3}{256}-\frac {487203129\,x^4}{512}-\frac {316246329\,x^5}{320}-\frac {53031699\,x^6}{64}-\frac {8399295\,x^7}{16}-\frac {14907321\,x^8}{64}-\frac {256365\,x^9}{4}-\frac {32805\,x^{10}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*x + 2)^8*(5*x + 3)^2)/(2*x - 1),x)

[Out]

- (695181625*x)/1024 - (697540921*log(x - 1/2))/2048 - (677093689*x^2)/1024 - (204901139*x^3)/256 - (487203129
*x^4)/512 - (316246329*x^5)/320 - (53031699*x^6)/64 - (8399295*x^7)/16 - (14907321*x^8)/64 - (256365*x^9)/4 -
(32805*x^10)/4

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sympy [A]  time = 0.13, size = 76, normalized size = 0.96 \[ - \frac {32805 x^{10}}{4} - \frac {256365 x^{9}}{4} - \frac {14907321 x^{8}}{64} - \frac {8399295 x^{7}}{16} - \frac {53031699 x^{6}}{64} - \frac {316246329 x^{5}}{320} - \frac {487203129 x^{4}}{512} - \frac {204901139 x^{3}}{256} - \frac {677093689 x^{2}}{1024} - \frac {695181625 x}{1024} - \frac {697540921 \log {\left (2 x - 1 \right )}}{2048} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**8*(3+5*x)**2/(1-2*x),x)

[Out]

-32805*x**10/4 - 256365*x**9/4 - 14907321*x**8/64 - 8399295*x**7/16 - 53031699*x**6/64 - 316246329*x**5/320 -
487203129*x**4/512 - 204901139*x**3/256 - 677093689*x**2/1024 - 695181625*x/1024 - 697540921*log(2*x - 1)/2048

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