3.1539 \(\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=69 \[ \frac{10935 x^7}{28}+\frac{11421 x^6}{4}+\frac{793881 x^5}{80}+\frac{1423899 x^4}{64}+\frac{2399985 x^3}{64}+\frac{873207 x^2}{16}+\frac{22333965 x}{256}+\frac{9058973}{512 (1-2 x)}+\frac{15647317}{256} \log (1-2 x) \]

[Out]

9058973/(512*(1 - 2*x)) + (22333965*x)/256 + (873207*x^2)/16 + (2399985*x^3)/64 + (1423899*x^4)/64 + (793881*x
^5)/80 + (11421*x^6)/4 + (10935*x^7)/28 + (15647317*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0366485, antiderivative size = 69, 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} \[ \frac{10935 x^7}{28}+\frac{11421 x^6}{4}+\frac{793881 x^5}{80}+\frac{1423899 x^4}{64}+\frac{2399985 x^3}{64}+\frac{873207 x^2}{16}+\frac{22333965 x}{256}+\frac{9058973}{512 (1-2 x)}+\frac{15647317}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

9058973/(512*(1 - 2*x)) + (22333965*x)/256 + (873207*x^2)/16 + (2399985*x^3)/64 + (1423899*x^4)/64 + (793881*x
^5)/80 + (11421*x^6)/4 + (10935*x^7)/28 + (15647317*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)^7 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{22333965}{256}+\frac{873207 x}{8}+\frac{7199955 x^2}{64}+\frac{1423899 x^3}{16}+\frac{793881 x^4}{16}+\frac{34263 x^5}{2}+\frac{10935 x^6}{4}+\frac{9058973}{256 (-1+2 x)^2}+\frac{15647317}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{9058973}{512 (1-2 x)}+\frac{22333965 x}{256}+\frac{873207 x^2}{16}+\frac{2399985 x^3}{64}+\frac{1423899 x^4}{64}+\frac{793881 x^5}{80}+\frac{11421 x^6}{4}+\frac{10935 x^7}{28}+\frac{15647317}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0133038, size = 64, normalized size = 0.93 \[ \frac{27993600 x^8+190667520 x^7+608985216 x^6+1239108192 x^5+1890599760 x^4+2567975760 x^3+4297526520 x^2-7692818118 x+2190624380 (2 x-1) \log (1-2 x)[phone]}{35840 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(1648903399 - 7692818118*x + 4297526520*x^2 + 2567975760*x^3 + 1890599760*x^4 + 1239108192*x^5 + 608985216*x^6
+ 190667520*x^7 + 27993600*x^8 + 2190624380*(-1 + 2*x)*Log[1 - 2*x])/(35840*(-1 + 2*x))

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Maple [A]  time = 0.005, size = 52, normalized size = 0.8 \begin{align*}{\frac{10935\,{x}^{7}}{28}}+{\frac{11421\,{x}^{6}}{4}}+{\frac{793881\,{x}^{5}}{80}}+{\frac{1423899\,{x}^{4}}{64}}+{\frac{2399985\,{x}^{3}}{64}}+{\frac{873207\,{x}^{2}}{16}}+{\frac{22333965\,x}{256}}+{\frac{15647317\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{9058973}{1024\,x-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)^2,x)

[Out]

10935/28*x^7+11421/4*x^6+793881/80*x^5+1423899/64*x^4+2399985/64*x^3+873207/16*x^2+22333965/256*x+15647317/256
*ln(2*x-1)-9058973/512/(2*x-1)

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Maxima [A]  time = 2.02203, size = 69, normalized size = 1. \begin{align*} \frac{10935}{28} \, x^{7} + \frac{11421}{4} \, x^{6} + \frac{793881}{80} \, x^{5} + \frac{1423899}{64} \, x^{4} + \frac{2399985}{64} \, x^{3} + \frac{873207}{16} \, x^{2} + \frac{22333965}{256} \, x - \frac{9058973}{512 \,{\left (2 \, x - 1\right )}} + \frac{15647317}{256} \, \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)^2,x, algorithm="maxima")

[Out]

10935/28*x^7 + 11421/4*x^6 + 793881/80*x^5 + 1423899/64*x^4 + 2399985/64*x^3 + 873207/16*x^2 + 22333965/256*x
- 9058973/512/(2*x - 1) + 15647317/256*log(2*x - 1)

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Fricas [A]  time = 1.19136, size = 262, normalized size = 3.8 \begin{align*} \frac{13996800 \, x^{8} + 95333760 \, x^{7} + 304492608 \, x^{6} + 619554096 \, x^{5} + 945299880 \, x^{4} + 1283987880 \, x^{3} + 2148763260 \, x^{2} + 1095312190 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1563377550 \, x - 317064055}{17920 \,{\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)^2,x, algorithm="fricas")

[Out]

1/17920*(13996800*x^8 + 95333760*x^7 + 304492608*x^6 + 619554096*x^5 + 945299880*x^4 + 1283987880*x^3 + 214876
3260*x^2 + 1095312190*(2*x - 1)*log(2*x - 1) - 1563377550*x - 317064055)/(2*x - 1)

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Sympy [A]  time = 0.112001, size = 61, normalized size = 0.88 \begin{align*} \frac{10935 x^{7}}{28} + \frac{11421 x^{6}}{4} + \frac{793881 x^{5}}{80} + \frac{1423899 x^{4}}{64} + \frac{2399985 x^{3}}{64} + \frac{873207 x^{2}}{16} + \frac{22333965 x}{256} + \frac{15647317 \log{\left (2 x - 1 \right )}}{256} - \frac{9058973}{1024 x - 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)**2,x)

[Out]

10935*x**7/28 + 11421*x**6/4 + 793881*x**5/80 + 1423899*x**4/64 + 2399985*x**3/64 + 873207*x**2/16 + 22333965*
x/256 + 15647317*log(2*x - 1)/256 - 9058973/(1024*x - 512)

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Giac [A]  time = 2.83046, size = 126, normalized size = 1.83 \begin{align*} \frac{3}{35840} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{788130}{2 \, x - 1} + \frac{7668108}{{\left (2 \, x - 1\right )}^{2}} + \frac{44406495}{{\left (2 \, x - 1\right )}^{3}} + \frac{171431400}{{\left (2 \, x - 1\right )}^{4}} + \frac{476478450}{{\left (2 \, x - 1\right )}^{5}} + \frac{1103547620}{{\left (2 \, x - 1\right )}^{6}} + 36450\right )} - \frac{9058973}{512 \,{\left (2 \, x - 1\right )}} - \frac{15647317}{256} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\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)^2,x, algorithm="giac")

[Out]

3/35840*(2*x - 1)^7*(788130/(2*x - 1) + 7668108/(2*x - 1)^2 + 44406495/(2*x - 1)^3 + 171431400/(2*x - 1)^4 + 4
76478450/(2*x - 1)^5 + 1103547620/(2*x - 1)^6 + 36450) - 9058973/512/(2*x - 1) - 15647317/256*log(1/2*abs(2*x
- 1)/(2*x - 1)^2)