\(\int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx\) [1435]

Optimal result

Integrand size = 20, antiderivative size = 65 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {8960669 x}{256}-\frac {8362653 x^2}{256}-\frac {2257119 x^3}{64}-\frac {4352157 x^4}{128}-\frac {2053917 x^5}{80}-\frac {218943 x^6}{16}-\frac {126117 x^7}{28}-\frac {10935 x^8}{16}-\frac {9058973}{512} \log (1-2 x) \]

[Out]

-8960669/256*x-8362653/256*x^2-2257119/64*x^3-4352157/128*x^4-2053917/80*x^5-218943/16*x^6-126117/28*x^7-10935
/16*x^8-9058973/512*ln(1-2*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 65, 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} \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {10935 x^8}{16}-\frac {126117 x^7}{28}-\frac {218943 x^6}{16}-\frac {2053917 x^5}{80}-\frac {4352157 x^4}{128}-\frac {2257119 x^3}{64}-\frac {8362653 x^2}{256}-\frac {8960669 x}{256}-\frac {9058973}{512} \log (1-2 x) \]

[In]

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

[Out]

(-8960669*x)/256 - (8362653*x^2)/256 - (2257119*x^3)/64 - (4352157*x^4)/128 - (2053917*x^5)/80 - (218943*x^6)/
16 - (126117*x^7)/28 - (10935*x^8)/16 - (9058973*Log[1 - 2*x])/512

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 {8960669}{256}-\frac {8362653 x}{128}-\frac {6771357 x^2}{64}-\frac {4352157 x^3}{32}-\frac {2053917 x^4}{16}-\frac {656829 x^5}{8}-\frac {126117 x^6}{4}-\frac {10935 x^7}{2}-\frac {9058973}{256 (-1+2 x)}\right ) \, dx \\ & = -\frac {8960669 x}{256}-\frac {8362653 x^2}{256}-\frac {2257119 x^3}{64}-\frac {4352157 x^4}{128}-\frac {2053917 x^5}{80}-\frac {218943 x^6}{16}-\frac {126117 x^7}{28}-\frac {10935 x^8}{16}-\frac {9058973}{512} \log (1-2 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.80 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=\frac {4767501827-5017974640 x-4683085680 x^2-5055946560 x^3-4874415840 x^4-3680619264 x^5-1961729280 x^6-645719040 x^7-97977600 x^8-2536512440 \log (1-2 x)}{143360} \]

[In]

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

[Out]

(4767501827 - 5017974640*x - 4683085680*x^2 - 5055946560*x^3 - 4874415840*x^4 - 3680619264*x^5 - 1961729280*x^
6 - 645719040*x^7 - 97977600*x^8 - 2536512440*Log[1 - 2*x])/143360

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {10935 x^{8}}{16}-\frac {126117 x^{7}}{28}-\frac {218943 x^{6}}{16}-\frac {2053917 x^{5}}{80}-\frac {4352157 x^{4}}{128}-\frac {2257119 x^{3}}{64}-\frac {8362653 x^{2}}{256}-\frac {8960669 x}{256}-\frac {9058973 \ln \left (x -\frac {1}{2}\right )}{512}\)	\(46\)
default	\(-\frac {10935 x^{8}}{16}-\frac {126117 x^{7}}{28}-\frac {218943 x^{6}}{16}-\frac {2053917 x^{5}}{80}-\frac {4352157 x^{4}}{128}-\frac {2257119 x^{3}}{64}-\frac {8362653 x^{2}}{256}-\frac {8960669 x}{256}-\frac {9058973 \ln \left (-1+2 x \right )}{512}\)	\(48\)
norman	\(-\frac {10935 x^{8}}{16}-\frac {126117 x^{7}}{28}-\frac {218943 x^{6}}{16}-\frac {2053917 x^{5}}{80}-\frac {4352157 x^{4}}{128}-\frac {2257119 x^{3}}{64}-\frac {8362653 x^{2}}{256}-\frac {8960669 x}{256}-\frac {9058973 \ln \left (-1+2 x \right )}{512}\)	\(48\)
risch	\(-\frac {10935 x^{8}}{16}-\frac {126117 x^{7}}{28}-\frac {218943 x^{6}}{16}-\frac {2053917 x^{5}}{80}-\frac {4352157 x^{4}}{128}-\frac {2257119 x^{3}}{64}-\frac {8362653 x^{2}}{256}-\frac {8960669 x}{256}-\frac {9058973 \ln \left (-1+2 x \right )}{512}\)	\(48\)
meijerg	\(-\frac {9058973 \ln \left (1-2 x \right )}{512}-2336 x -1036 x \left (6 x +6\right )-\frac {1575 x \left (16 x^{2}+12 x +12\right )}{2}-\frac {1197 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{8}-\frac {14553 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{160}-\frac {3159 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{640}-\frac {19197 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{35840}-\frac {243 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}\)	\(174\)

[In]

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

[Out]

-10935/16*x^8-126117/28*x^7-218943/16*x^6-2053917/80*x^5-4352157/128*x^4-2257119/64*x^3-8362653/256*x^2-896066
9/256*x-9058973/512*ln(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-10935/16*x^8 - 126117/28*x^7 - 218943/16*x^6 - 2053917/80*x^5 - 4352157/128*x^4 - 2257119/64*x^3 - 8362653/25
6*x^2 - 8960669/256*x - 9058973/512*log(2*x - 1)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=- \frac {10935 x^{8}}{16} - \frac {126117 x^{7}}{28} - \frac {218943 x^{6}}{16} - \frac {2053917 x^{5}}{80} - \frac {4352157 x^{4}}{128} - \frac {2257119 x^{3}}{64} - \frac {8362653 x^{2}}{256} - \frac {8960669 x}{256} - \frac {9058973 \log {\left (2 x - 1 \right )}}{512} \]

[In]

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

[Out]

-10935*x**8/16 - 126117*x**7/28 - 218943*x**6/16 - 2053917*x**5/80 - 4352157*x**4/128 - 2257119*x**3/64 - 8362
653*x**2/256 - 8960669*x/256 - 9058973*log(2*x - 1)/512

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-10935/16*x^8 - 126117/28*x^7 - 218943/16*x^6 - 2053917/80*x^5 - 4352157/128*x^4 - 2257119/64*x^3 - 8362653/25
6*x^2 - 8960669/256*x - 9058973/512*log(2*x - 1)

Giac [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[In]

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

[Out]

-10935/16*x^8 - 126117/28*x^7 - 218943/16*x^6 - 2053917/80*x^5 - 4352157/128*x^4 - 2257119/64*x^3 - 8362653/25
6*x^2 - 8960669/256*x - 9058973/512*log(abs(2*x - 1))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx=-\frac {8960669\,x}{256}-\frac {9058973\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {8362653\,x^2}{256}-\frac {2257119\,x^3}{64}-\frac {4352157\,x^4}{128}-\frac {2053917\,x^5}{80}-\frac {218943\,x^6}{16}-\frac {126117\,x^7}{28}-\frac {10935\,x^8}{16} \]

[In]

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

[Out]

- (8960669*x)/256 - (9058973*log(x - 1/2))/512 - (8362653*x^2)/256 - (2257119*x^3)/64 - (4352157*x^4)/128 - (2
053917*x^5)/80 - (218943*x^6)/16 - (126117*x^7)/28 - (10935*x^8)/16