3.1632 \(\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=66 \[ -\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x) \]

[Out]

1294139/(512*(1 - 2*x)^2) - 3916031/(256*(1 - 2*x)) - (2431647*x)/128 - (461835*x^2)/64 - (10611*x^3)/4 - (444
69*x^4)/64 - (729*x^5)/8 - (5078115*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0350226, antiderivative size = 66, 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} \[ -\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

1294139/(512*(1 - 2*x)^2) - 3916031/(256*(1 - 2*x)) - (2431647*x)/128 - (461835*x^2)/64 - (10611*x^3)/4 - (444
69*x^4)/64 - (729*x^5)/8 - (5078115*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)^3} \, dx &=\int \left (-\frac{2431647}{128}-\frac{461835 x}{32}-\frac{31833 x^2}{4}-\frac{44469 x^3}{16}-\frac{3645 x^4}{8}-\frac{1294139}{128 (-1+2 x)^3}-\frac{3916031}{128 (-1+2 x)^2}-\frac{5078115}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{1294139}{512 (1-2 x)^2}-\frac{3916031}{256 (1-2 x)}-\frac{2431647 x}{128}-\frac{461835 x^2}{64}-\frac{10611 x^3}{4}-\frac{44469 x^4}{64}-\frac{729 x^5}{8}-\frac{5078115}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0164457, size = 61, normalized size = 0.92 \[ -\frac{373248 x^7+2472768 x^6+8112960 x^5+19403280 x^4+50971680 x^3-118266804 x^2+35968388 x+20312460 (1-2 x)^2 \log (1-2 x)+1114981}{1024 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(1114981 + 35968388*x - 118266804*x^2 + 50971680*x^3 + 19403280*x^4 + 8112960*x^5 + 2472768*x^6 + 373248*x^7
+ 20312460*(1 - 2*x)^2*Log[1 - 2*x])/(1024*(1 - 2*x)^2)

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Maple [A]  time = 0.006, size = 51, normalized size = 0.8 \begin{align*} -{\frac{729\,{x}^{5}}{8}}-{\frac{44469\,{x}^{4}}{64}}-{\frac{10611\,{x}^{3}}{4}}-{\frac{461835\,{x}^{2}}{64}}-{\frac{2431647\,x}{128}}-{\frac{5078115\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{1294139}{512\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{3916031}{512\,x-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)^3,x)

[Out]

-729/8*x^5-44469/64*x^4-10611/4*x^3-461835/64*x^2-2431647/128*x-5078115/256*ln(2*x-1)+1294139/512/(2*x-1)^2+39
16031/256/(2*x-1)

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Maxima [A]  time = 1.06351, size = 69, normalized size = 1.05 \begin{align*} -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{5078115}{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)^3,x, algorithm="maxima")

[Out]

-729/8*x^5 - 44469/64*x^4 - 10611/4*x^3 - 461835/64*x^2 - 2431647/128*x + 16807/512*(932*x - 389)/(4*x^2 - 4*x
+ 1) - 5078115/256*log(2*x - 1)

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Fricas [A]  time = 1.44726, size = 236, normalized size = 3.58 \begin{align*} -\frac{186624 \, x^{7} + 1236384 \, x^{6} + 4056480 \, x^{5} + 9701640 \, x^{4} + 25485840 \, x^{3} - 35211672 \, x^{2} + 10156230 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 5937536 \, x + 6537923}{512 \,{\left (4 \, x^{2} - 4 \, 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)^3,x, algorithm="fricas")

[Out]

-1/512*(186624*x^7 + 1236384*x^6 + 4056480*x^5 + 9701640*x^4 + 25485840*x^3 - 35211672*x^2 + 10156230*(4*x^2 -
4*x + 1)*log(2*x - 1) - 5937536*x + 6537923)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.128977, size = 56, normalized size = 0.85 \begin{align*} - \frac{729 x^{5}}{8} - \frac{44469 x^{4}}{64} - \frac{10611 x^{3}}{4} - \frac{461835 x^{2}}{64} - \frac{2431647 x}{128} + \frac{15664124 x - 6537923}{2048 x^{2} - 2048 x + 512} - \frac{5078115 \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)**3,x)

[Out]

-729*x**5/8 - 44469*x**4/64 - 10611*x**3/4 - 461835*x**2/64 - 2431647*x/128 + (15664124*x - 6537923)/(2048*x**
2 - 2048*x + 512) - 5078115*log(2*x - 1)/256

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Giac [A]  time = 3.27244, size = 63, normalized size = 0.95 \begin{align*} -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (2 \, x - 1\right )}^{2}} - \frac{5078115}{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)^3,x, algorithm="giac")

[Out]

-729/8*x^5 - 44469/64*x^4 - 10611/4*x^3 - 461835/64*x^2 - 2431647/128*x + 16807/512*(932*x - 389)/(2*x - 1)^2
- 5078115/256*log(abs(2*x - 1))