3.1630 \(\int \frac {(2+3 x)^8 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=80 \[ -\frac {32805 x^7}{56}-\frac {162567 x^6}{32}-\frac {213597 x^5}{10}-\frac {7568235 x^4}{128}-\frac {16042509 x^3}{128}-\frac {118841283 x^2}{512}-\frac {120864213 x}{256}-\frac {246239357}{1024 (1-2 x)}+\frac {63412811}{2048 (1-2 x)^2}-\frac {106237047}{256} \log (1-2 x) \]

[Out]

63412811/2048/(1-2*x)^2-246239357/1024/(1-2*x)-120864213/256*x-118841283/512*x^2-16042509/128*x^3-7568235/128*
x^4-213597/10*x^5-162567/32*x^6-32805/56*x^7-106237047/256*ln(1-2*x)

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Rubi [A]  time = 0.05, antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {32805 x^7}{56}-\frac {162567 x^6}{32}-\frac {213597 x^5}{10}-\frac {7568235 x^4}{128}-\frac {16042509 x^3}{128}-\frac {118841283 x^2}{512}-\frac {120864213 x}{256}-\frac {246239357}{1024 (1-2 x)}+\frac {63412811}{2048 (1-2 x)^2}-\frac {106237047}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

63412811/(2048*(1 - 2*x)^2) - 246239357/(1024*(1 - 2*x)) - (120864213*x)/256 - (118841283*x^2)/512 - (16042509
*x^3)/128 - (7568235*x^4)/128 - (213597*x^5)/10 - (162567*x^6)/32 - (32805*x^7)/56 - (106237047*Log[1 - 2*x])/
256

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)^3} \, dx &=\int \left (-\frac {120864213}{256}-\frac {118841283 x}{256}-\frac {48127527 x^2}{128}-\frac {7568235 x^3}{32}-\frac {213597 x^4}{2}-\frac {487701 x^5}{16}-\frac {32805 x^6}{8}-\frac {63412811}{512 (-1+2 x)^3}-\frac {246239357}{512 (-1+2 x)^2}-\frac {106237047}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {63412811}{2048 (1-2 x)^2}-\frac {246239357}{1024 (1-2 x)}-\frac {120864213 x}{256}-\frac {118841283 x^2}{512}-\frac {16042509 x^3}{128}-\frac {7568235 x^4}{128}-\frac {213597 x^5}{10}-\frac {162567 x^6}{32}-\frac {32805 x^7}{56}-\frac {106237047}{256} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 71, normalized size = 0.89 \[ -\frac {83980800 x^9+644319360 x^8+2354821632 x^7+5596371648 x^6+10256718528 x^5+17427054960 x^4+38900302560 x^3-104409393876 x^2+44728559236 x+14873186580 (1-2 x)^2 \log (1-2 x)-3752427799}{35840 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-1/35840*(-3752427799 + 44728559236*x - 104409393876*x^2 + 38900302560*x^3 + 17427054960*x^4 + 10256718528*x^5
+ 5596371648*x^6 + 2354821632*x^7 + 644319360*x^8 + 83980800*x^9 + 14873186580*(1 - 2*x)^2*Log[1 - 2*x])/(1 -
2*x)^2

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fricas [A]  time = 0.61, size = 77, normalized size = 0.96 \[ -\frac {167961600 \, x^{9} + 1288638720 \, x^{8} + 4709643264 \, x^{7} + 11192743296 \, x^{6} + 20513437056 \, x^{5} + 34854109920 \, x^{4} + 77800605120 \, x^{3} - 118730138940 \, x^{2} + 29746373160 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 631530340 \, x + 15017306605}{71680 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/71680*(167961600*x^9 + 1288638720*x^8 + 4709643264*x^7 + 11192743296*x^6 + 20513437056*x^5 + 34854109920*x^
4 + 77800605120*x^3 - 118730138940*x^2 + 29746373160*(4*x^2 - 4*x + 1)*log(2*x - 1) - 631530340*x + 1501730660
5)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.27, size = 57, normalized size = 0.71 \[ -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {106237047}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-32805/56*x^7 - 162567/32*x^6 - 213597/10*x^5 - 7568235/128*x^4 - 16042509/128*x^3 - 118841283/512*x^2 - 12086
4213/256*x + 823543/2048*(1196*x - 521)/(2*x - 1)^2 - 106237047/256*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 61, normalized size = 0.76 \[ -\frac {32805 x^{7}}{56}-\frac {162567 x^{6}}{32}-\frac {213597 x^{5}}{10}-\frac {7568235 x^{4}}{128}-\frac {16042509 x^{3}}{128}-\frac {118841283 x^{2}}{512}-\frac {120864213 x}{256}-\frac {106237047 \ln \left (2 x -1\right )}{256}+\frac {63412811}{2048 \left (2 x -1\right )^{2}}+\frac {246239357}{1024 \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-32805/56*x^7-162567/32*x^6-213597/10*x^5-7568235/128*x^4-16042509/128*x^3-118841283/512*x^2-120864213/256*x+6
3412811/2048/(2*x-1)^2+246239357/1024/(2*x-1)-106237047/256*ln(2*x-1)

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maxima [A]  time = 0.50, size = 61, normalized size = 0.76 \[ -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {106237047}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-32805/56*x^7 - 162567/32*x^6 - 213597/10*x^5 - 7568235/128*x^4 - 16042509/128*x^3 - 118841283/512*x^2 - 12086
4213/256*x + 823543/2048*(1196*x - 521)/(4*x^2 - 4*x + 1) - 106237047/256*log(2*x - 1)

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mupad [B]  time = 0.04, size = 56, normalized size = 0.70 \[ \frac {\frac {246239357\,x}{2048}-\frac {429065903}{8192}}{x^2-x+\frac {1}{4}}-\frac {106237047\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {120864213\,x}{256}-\frac {118841283\,x^2}{512}-\frac {16042509\,x^3}{128}-\frac {7568235\,x^4}{128}-\frac {213597\,x^5}{10}-\frac {162567\,x^6}{32}-\frac {32805\,x^7}{56} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((246239357*x)/2048 - 429065903/8192)/(x^2 - x + 1/4) - (106237047*log(x - 1/2))/256 - (120864213*x)/256 - (11
8841283*x^2)/512 - (16042509*x^3)/128 - (7568235*x^4)/128 - (213597*x^5)/10 - (162567*x^6)/32 - (32805*x^7)/56

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sympy [A]  time = 0.15, size = 71, normalized size = 0.89 \[ - \frac {32805 x^{7}}{56} - \frac {162567 x^{6}}{32} - \frac {213597 x^{5}}{10} - \frac {7568235 x^{4}}{128} - \frac {16042509 x^{3}}{128} - \frac {118841283 x^{2}}{512} - \frac {120864213 x}{256} - \frac {429065903 - 984957428 x}{8192 x^{2} - 8192 x + 2048} - \frac {106237047 \log {\left (2 x - 1 \right )}}{256} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-32805*x**7/56 - 162567*x**6/32 - 213597*x**5/10 - 7568235*x**4/128 - 16042509*x**3/128 - 118841283*x**2/512 -
120864213*x/256 - (429065903 - 984957428*x)/(8192*x**2 - 8192*x + 2048) - 106237047*log(2*x - 1)/256

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