3.1435 \(\int \frac{(2+3 x)^7 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=65 \[ -\frac{10935 x^8}{16}-\frac{126117 x^7}{28}-\frac{218943 x^6}{16}-\frac{2053917 x^5}{80}-\frac{4352157 x^4}{128}-\frac{2257119 x^3}{64}-\frac{8362653 x^2}{256}-\frac{8960669 x}{256}-\frac{9058973}{512} \log (1-2 x) \]

[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

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Rubi [A]  time = 0.0249565, antiderivative size = 65, 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} \[ -\frac{10935 x^8}{16}-\frac{126117 x^7}{28}-\frac{218943 x^6}{16}-\frac{2053917 x^5}{80}-\frac{4352157 x^4}{128}-\frac{2257119 x^3}{64}-\frac{8362653 x^2}{256}-\frac{8960669 x}{256}-\frac{9058973}{512} \log (1-2 x) \]

Antiderivative was successfully verified.

[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 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)^7 (3+5 x)}{1-2 x} \, dx &=\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]  time = 0.0146071, size = 52, normalized size = 0.8 \[ \frac{-97977600 x^8-645719040 x^7-1961729280 x^6-3680619264 x^5-4874415840 x^4-5055946560 x^3-4683085680 x^2-5017974640 x-2536512440 \log (1-2 x)[phone]}{143360} \]

Antiderivative was successfully verified.

[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

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Maple [A]  time = 0.002, size = 48, normalized size = 0.7 \begin{align*} -{\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 ( 2\,x-1 \right ) }{512}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[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(2*x-1)

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Maxima [A]  time = 1.03739, size = 63, normalized size = 0.97 \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Fricas [A]  time = 1.20157, size = 216, normalized size = 3.32 \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Sympy [A]  time = 0.102434, size = 63, normalized size = 0.97 \begin{align*} - \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} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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Giac [A]  time = 2.05742, size = 65, normalized size = 1. \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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))