3.1434 \(\int \frac{(2+3 x)^8 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=72 \[ -\frac{3645 x^9}{2}-\frac{422091 x^8}{32}-\frac{353565 x^7}{8}-\frac{2929689 x^6}{32}-\frac{21272139 x^5}{160}-\frac{37722699 x^4}{256}-\frac{17391129 x^3}{128}-\frac{60332619 x^2}{512}-\frac{63019595 x}{512}-\frac{63412811 \log (1-2 x)}{1024} \]

[Out]

(-63019595*x)/512 - (60332619*x^2)/512 - (17391129*x^3)/128 - (37722699*x^4)/256 - (21272139*x^5)/160 - (29296
89*x^6)/32 - (353565*x^7)/8 - (422091*x^8)/32 - (3645*x^9)/2 - (63412811*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0277745, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{3645 x^9}{2}-\frac{422091 x^8}{32}-\frac{353565 x^7}{8}-\frac{2929689 x^6}{32}-\frac{21272139 x^5}{160}-\frac{37722699 x^4}{256}-\frac{17391129 x^3}{128}-\frac{60332619 x^2}{512}-\frac{63019595 x}{512}-\frac{63412811 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-63019595*x)/512 - (60332619*x^2)/512 - (17391129*x^3)/128 - (37722699*x^4)/256 - (21272139*x^5)/160 - (29296
89*x^6)/32 - (353565*x^7)/8 - (422091*x^8)/32 - (3645*x^9)/2 - (63412811*Log[1 - 2*x])/1024

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^8 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{63019595}{512}-\frac{60332619 x}{256}-\frac{52173387 x^2}{128}-\frac{37722699 x^3}{64}-\frac{21272139 x^4}{32}-\frac{8789067 x^5}{16}-\frac{2474955 x^6}{8}-\frac{422091 x^7}{4}-\frac{32805 x^8}{2}-\frac{63412811}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac{63019595 x}{512}-\frac{60332619 x^2}{512}-\frac{17391129 x^3}{128}-\frac{37722699 x^4}{256}-\frac{21272139 x^5}{160}-\frac{2929689 x^6}{32}-\frac{353565 x^7}{8}-\frac{422091 x^8}{32}-\frac{3645 x^9}{2}-\frac{63412811 \log (1-2 x)}{1024}\\ \end{align*}

Mathematica [A]  time = 0.0167705, size = 57, normalized size = 0.79 \[ \frac{-74649600 x^9-540276480 x^8-1810252800 x^7-3750001920 x^6-5445667584 x^5-6035631840 x^4-5565161280 x^3-4826609520 x^2-5041567600 x-2536512440 \log (1-2 x)[phone]}{40960} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(5045478077 - 5041567600*x - 4826609520*x^2 - 5565161280*x^3 - 6035631840*x^4 - 5445667584*x^5 - 3750001920*x^
6 - 1810252800*x^7 - 540276480*x^8 - 74649600*x^9 - 2536512440*Log[1 - 2*x])/40960

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Maple [A]  time = 0.003, size = 53, normalized size = 0.7 \begin{align*} -{\frac{3645\,{x}^{9}}{2}}-{\frac{422091\,{x}^{8}}{32}}-{\frac{353565\,{x}^{7}}{8}}-{\frac{2929689\,{x}^{6}}{32}}-{\frac{21272139\,{x}^{5}}{160}}-{\frac{37722699\,{x}^{4}}{256}}-{\frac{17391129\,{x}^{3}}{128}}-{\frac{60332619\,{x}^{2}}{512}}-{\frac{63019595\,x}{512}}-{\frac{63412811\,\ln \left ( 2\,x-1 \right ) }{1024}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3645/2*x^9-422091/32*x^8-353565/8*x^7-2929689/32*x^6-21272139/160*x^5-37722699/256*x^4-17391129/128*x^3-60332
619/512*x^2-63019595/512*x-63412811/1024*ln(2*x-1)

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Maxima [A]  time = 1.06692, size = 70, normalized size = 0.97 \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \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)/(1-2*x),x, algorithm="maxima")

[Out]

-3645/2*x^9 - 422091/32*x^8 - 353565/8*x^7 - 2929689/32*x^6 - 21272139/160*x^5 - 37722699/256*x^4 - 17391129/1
28*x^3 - 60332619/512*x^2 - 63019595/512*x - 63412811/1024*log(2*x - 1)

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Fricas [A]  time = 1.30488, size = 247, normalized size = 3.43 \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \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)/(1-2*x),x, algorithm="fricas")

[Out]

-3645/2*x^9 - 422091/32*x^8 - 353565/8*x^7 - 2929689/32*x^6 - 21272139/160*x^5 - 37722699/256*x^4 - 17391129/1
28*x^3 - 60332619/512*x^2 - 63019595/512*x - 63412811/1024*log(2*x - 1)

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Sympy [A]  time = 0.105237, size = 70, normalized size = 0.97 \begin{align*} - \frac{3645 x^{9}}{2} - \frac{422091 x^{8}}{32} - \frac{353565 x^{7}}{8} - \frac{2929689 x^{6}}{32} - \frac{21272139 x^{5}}{160} - \frac{37722699 x^{4}}{256} - \frac{17391129 x^{3}}{128} - \frac{60332619 x^{2}}{512} - \frac{63019595 x}{512} - \frac{63412811 \log{\left (2 x - 1 \right )}}{1024} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3645*x**9/2 - 422091*x**8/32 - 353565*x**7/8 - 2929689*x**6/32 - 21272139*x**5/160 - 37722699*x**4/256 - 1739
1129*x**3/128 - 60332619*x**2/512 - 63019595*x/512 - 63412811*log(2*x - 1)/1024

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Giac [A]  time = 1.94187, size = 72, normalized size = 1. \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{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)^8*(3+5*x)/(1-2*x),x, algorithm="giac")

[Out]

-3645/2*x^9 - 422091/32*x^8 - 353565/8*x^7 - 2929689/32*x^6 - 21272139/160*x^5 - 37722699/256*x^4 - 17391129/1
28*x^3 - 60332619/512*x^2 - 63019595/512*x - 63412811/1024*log(abs(2*x - 1))