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

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

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 58, 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} \begin {gather*} -\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) \end {gather*}

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 = 0.02, size = 47, normalized size = 0.81 \begin {gather*} \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} \end {gather*}

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

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^6 (3+5 x)}{1-2 x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.80, size = 42, normalized size = 0.72 \begin {gather*} -\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 {gather*}

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)

________________________________________________________________________________________

giac [A]  time = 1.06, size = 43, normalized size = 0.74 \begin {gather*} -\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 {gather*}

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))

________________________________________________________________________________________

maple [A]  time = 0.00, size = 43, normalized size = 0.74 \begin {gather*} -\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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

________________________________________________________________________________________

maxima [A]  time = 0.69, size = 42, normalized size = 0.72 \begin {gather*} -\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 {gather*}

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)

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 40, normalized size = 0.69 \begin {gather*} -\frac {1269563\,x}{128}-\frac {1294139\,\ln \left (x-\frac {1}{2}\right )}{256}-\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- (1269563*x)/128 - (1294139*log(x - 1/2))/256 - (1138491*x^2)/128 - (279657*x^3)/32 - (458811*x^4)/64 - (1693
71*x^5)/40 - (12393*x^6)/8 - (3645*x^7)/14

________________________________________________________________________________________

sympy [A]  time = 0.11, size = 56, normalized size = 0.97 \begin {gather*} - \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 {gather*}

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

________________________________________________________________________________________