\(\int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx\) [1434]

Optimal result

Integrand size = 20, antiderivative size = 72 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {63019595 x}{512}-\frac {60332619 x^2}{512}-\frac {17391129 x^3}{128}-\frac {37722699 x^4}{256}-\frac {21272139 x^5}{160}-\frac {2929689 x^6}{32}-\frac {353565 x^7}{8}-\frac {422091 x^8}{32}-\frac {3645 x^9}{2}-\frac {63412811 \log (1-2 x)}{1024} \]

[Out]

-63019595/512*x-60332619/512*x^2-17391129/128*x^3-37722699/256*x^4-21272139/160*x^5-2929689/32*x^6-353565/8*x^
7-422091/32*x^8-3645/2*x^9-63412811/1024*ln(1-2*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {3645 x^9}{2}-\frac {422091 x^8}{32}-\frac {353565 x^7}{8}-\frac {2929689 x^6}{32}-\frac {21272139 x^5}{160}-\frac {37722699 x^4}{256}-\frac {17391129 x^3}{128}-\frac {60332619 x^2}{512}-\frac {63019595 x}{512}-\frac {63412811 \log (1-2 x)}{1024} \]

[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 78

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*} \text {integral}& = \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] (verified)

Time = 0.02 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.79 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=\frac {5045478077-5041567600 x-4826609520 x^2-5565161280 x^3-6035631840 x^4-5445667584 x^5-3750001920 x^6-1810252800 x^7-540276480 x^8-74649600 x^9-2536512440 \log (1-2 x)}{40960} \]

[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

Maple [A] (verified)

Time = 2.54 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {3645 x^{9}}{2}-\frac {422091 x^{8}}{32}-\frac {353565 x^{7}}{8}-\frac {2929689 x^{6}}{32}-\frac {21272139 x^{5}}{160}-\frac {37722699 x^{4}}{256}-\frac {17391129 x^{3}}{128}-\frac {60332619 x^{2}}{512}-\frac {63019595 x}{512}-\frac {63412811 \ln \left (x -\frac {1}{2}\right )}{1024}\)	\(51\)
default	\(-\frac {3645 x^{9}}{2}-\frac {422091 x^{8}}{32}-\frac {353565 x^{7}}{8}-\frac {2929689 x^{6}}{32}-\frac {21272139 x^{5}}{160}-\frac {37722699 x^{4}}{256}-\frac {17391129 x^{3}}{128}-\frac {60332619 x^{2}}{512}-\frac {63019595 x}{512}-\frac {63412811 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
norman	\(-\frac {3645 x^{9}}{2}-\frac {422091 x^{8}}{32}-\frac {353565 x^{7}}{8}-\frac {2929689 x^{6}}{32}-\frac {21272139 x^{5}}{160}-\frac {37722699 x^{4}}{256}-\frac {17391129 x^{3}}{128}-\frac {60332619 x^{2}}{512}-\frac {63019595 x}{512}-\frac {63412811 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
risch	\(-\frac {3645 x^{9}}{2}-\frac {422091 x^{8}}{32}-\frac {353565 x^{7}}{8}-\frac {2929689 x^{6}}{32}-\frac {21272139 x^{5}}{160}-\frac {37722699 x^{4}}{256}-\frac {17391129 x^{3}}{128}-\frac {60332619 x^{2}}{512}-\frac {63019595 x}{512}-\frac {63412811 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
meijerg	\(-\frac {63412811 \ln \left (1-2 x \right )}{1024}-5248 x -\frac {2349 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{80}-\frac {2673 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{560}-\frac {21627 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{71680}-\frac {8127 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{20}-2656 x \left (6 x +6\right )-2352 x \left (16 x^{2}+12 x +12\right )-\frac {1071 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{2}-\frac {729 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{28672}\)	\(217\)

[In]

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

[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(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \log \left (2 \, x - 1\right ) \]

[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)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=- \frac {3645 x^{9}}{2} - \frac {422091 x^{8}}{32} - \frac {353565 x^{7}}{8} - \frac {2929689 x^{6}}{32} - \frac {21272139 x^{5}}{160} - \frac {37722699 x^{4}}{256} - \frac {17391129 x^{3}}{128} - \frac {60332619 x^{2}}{512} - \frac {63019595 x}{512} - \frac {63412811 \log {\left (2 x - 1 \right )}}{1024} \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \log \left (2 \, x - 1\right ) \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[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))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx=-\frac {63019595\,x}{512}-\frac {63412811\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {60332619\,x^2}{512}-\frac {17391129\,x^3}{128}-\frac {37722699\,x^4}{256}-\frac {21272139\,x^5}{160}-\frac {2929689\,x^6}{32}-\frac {353565\,x^7}{8}-\frac {422091\,x^8}{32}-\frac {3645\,x^9}{2} \]

[In]

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

[Out]

- (63019595*x)/512 - (63412811*log(x - 1/2))/1024 - (60332619*x^2)/512 - (17391129*x^3)/128 - (37722699*x^4)/2
56 - (21272139*x^5)/160 - (2929689*x^6)/32 - (353565*x^7)/8 - (422091*x^8)/32 - (3645*x^9)/2