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*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

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Rubi [A]  time = 0.0371611, antiderivative size = 79, 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} \[ -\frac{32805 x^{10}}{4}-\frac{256365 x^9}{4}-\frac{14907321 x^8}{64}-\frac{8399295 x^7}{16}-\frac{53031699 x^6}{64}-\frac{316246329 x^5}{320}-\frac{487203129 x^4}{512}-\frac{204901139 x^3}{256}-\frac{677093689 x^2}{1024}-\frac{695181625 x}{1024}-\frac{697540921 \log (1-2 x)}{2048} \]

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*}

Mathematica [A]  time = 0.0145662, 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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Maple [A]  time = 0.003, size = 58, normalized size = 0.7 \begin{align*} -{\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}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^8*(3+5*x)^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 = 1.06897, size = 77, normalized size = 0.97 \begin{align*} -\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 ) \end{align*}

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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Fricas [A]  time = 1.56179, size = 288, normalized size = 3.65 \begin{align*} -\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 ) \end{align*}

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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Sympy [A]  time = 0.112183, size = 76, normalized size = 0.96 \begin{align*} - \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} \end{align*}

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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Giac [A]  time = 2.52304, size = 78, normalized size = 0.99 \begin{align*} -\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 ) \end{align*}

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))