3.1436 \(\int \frac{(2+3 x)^6 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=58 \[ -\frac{3645 x^7}{14}-\frac{12393 x^6}{8}-\frac{169371 x^5}{40}-\frac{458811 x^4}{64}-\frac{279657 x^3}{32}-\frac{1138491 x^2}{128}-\frac{1269563 x}{128}-\frac{1294139}{256} \log (1-2 x) \]

[Out]

(-1269563*x)/128 - (1138491*x^2)/128 - (279657*x^3)/32 - (458811*x^4)/64 - (169371*x^5)/40 - (12393*x^6)/8 - (
3645*x^7)/14 - (1294139*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0224031, antiderivative size = 58, 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} \[ -\frac{3645 x^7}{14}-\frac{12393 x^6}{8}-\frac{169371 x^5}{40}-\frac{458811 x^4}{64}-\frac{279657 x^3}{32}-\frac{1138491 x^2}{128}-\frac{1269563 x}{128}-\frac{1294139}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x),x]

[Out]

(-1269563*x)/128 - (1138491*x^2)/128 - (279657*x^3)/32 - (458811*x^4)/64 - (169371*x^5)/40 - (12393*x^6)/8 - (
3645*x^7)/14 - (1294139*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)^6 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{1269563}{128}-\frac{1138491 x}{64}-\frac{838971 x^2}{32}-\frac{458811 x^3}{16}-\frac{169371 x^4}{8}-\frac{37179 x^5}{4}-\frac{3645 x^6}{2}-\frac{1294139}{128 (-1+2 x)}\right ) \, dx\\ &=-\frac{1269563 x}{128}-\frac{1138491 x^2}{128}-\frac{279657 x^3}{32}-\frac{458811 x^4}{64}-\frac{169371 x^5}{40}-\frac{12393 x^6}{8}-\frac{3645 x^7}{14}-\frac{1294139}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0145983, size = 47, normalized size = 0.81 \[ \frac{-9331200 x^7-55520640 x^6-151756416 x^5-256934160 x^4-313215840 x^3-318777480 x^2-355477640 x-181179460 \log (1-2 x)[phone]}{35840} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x),x]

[Out]

(318326353 - 355477640*x - 318777480*x^2 - 313215840*x^3 - 256934160*x^4 - 151756416*x^5 - 55520640*x^6 - 9331
200*x^7 - 181179460*Log[1 - 2*x])/35840

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Maple [A]  time = 0.003, size = 43, normalized size = 0.7 \begin{align*} -{\frac{3645\,{x}^{7}}{14}}-{\frac{12393\,{x}^{6}}{8}}-{\frac{169371\,{x}^{5}}{40}}-{\frac{458811\,{x}^{4}}{64}}-{\frac{279657\,{x}^{3}}{32}}-{\frac{1138491\,{x}^{2}}{128}}-{\frac{1269563\,x}{128}}-{\frac{1294139\,\ln \left ( 2\,x-1 \right ) }{256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^6*(3+5*x)/(1-2*x),x)

[Out]

-3645/14*x^7-12393/8*x^6-169371/40*x^5-458811/64*x^4-279657/32*x^3-1138491/128*x^2-1269563/128*x-1294139/256*l
n(2*x-1)

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Maxima [A]  time = 1.02095, size = 57, normalized size = 0.98 \begin{align*} -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)/(1-2*x),x, algorithm="maxima")

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 1138491/128*x^2 - 1269563/128*x -
1294139/256*log(2*x - 1)

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Fricas [A]  time = 1.35512, size = 185, normalized size = 3.19 \begin{align*} -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)/(1-2*x),x, algorithm="fricas")

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 1138491/128*x^2 - 1269563/128*x -
1294139/256*log(2*x - 1)

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Sympy [A]  time = 0.099122, size = 56, normalized size = 0.97 \begin{align*} - \frac{3645 x^{7}}{14} - \frac{12393 x^{6}}{8} - \frac{169371 x^{5}}{40} - \frac{458811 x^{4}}{64} - \frac{279657 x^{3}}{32} - \frac{1138491 x^{2}}{128} - \frac{1269563 x}{128} - \frac{1294139 \log{\left (2 x - 1 \right )}}{256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**6*(3+5*x)/(1-2*x),x)

[Out]

-3645*x**7/14 - 12393*x**6/8 - 169371*x**5/40 - 458811*x**4/64 - 279657*x**3/32 - 1138491*x**2/128 - 1269563*x
/128 - 1294139*log(2*x - 1)/256

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Giac [A]  time = 2.59211, size = 58, normalized size = 1. \begin{align*} -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \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)^6*(3+5*x)/(1-2*x),x, algorithm="giac")

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 1138491/128*x^2 - 1269563/128*x -
1294139/256*log(abs(2*x - 1))