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

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

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Rubi [A]  time = 0.04, antiderivative size = 66, 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 {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) \end {gather*}

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*}

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Mathematica [A]  time = 0.02, size = 61, normalized size = 0.92 \begin {gather*} -\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} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/1024*(1114981 + 35968388*x - 118266804*x^2 + 50971680*x^3 + 19403280*x^4 + 8112960*x^5 + 2472768*x^6 + 3732
48*x^7 + 20312460*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2

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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)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.94, size = 67, normalized size = 1.02 \begin {gather*} -\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 {gather*}

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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giac [A]  time = 1.16, size = 47, normalized size = 0.71 \begin {gather*} -\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 {gather*}

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))

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maple [A]  time = 0.01, size = 51, normalized size = 0.77 \begin {gather*} -\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}{256 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^6*(5*x+3)/(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+1294139/512/(2*x-1)^2+3916031/256/(2*x-1)-5078
115/256*ln(2*x-1)

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maxima [A]  time = 0.64, size = 51, normalized size = 0.77 \begin {gather*} -\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 {gather*}

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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mupad [B]  time = 0.03, size = 46, normalized size = 0.70 \begin {gather*} \frac {\frac {3916031\,x}{512}-\frac {6537923}{2048}}{x^2-x+\frac {1}{4}}-\frac {5078115\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {2431647\,x}{128}-\frac {461835\,x^2}{64}-\frac {10611\,x^3}{4}-\frac {44469\,x^4}{64}-\frac {729\,x^5}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((3916031*x)/512 - 6537923/2048)/(x^2 - x + 1/4) - (5078115*log(x - 1/2))/256 - (2431647*x)/128 - (461835*x^2)
/64 - (10611*x^3)/4 - (44469*x^4)/64 - (729*x^5)/8

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sympy [A]  time = 0.15, size = 58, normalized size = 0.88 \begin {gather*} - \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 {6537923 - 15664124 x}{2048 x^{2} - 2048 x + 512} - \frac {5078115 \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)**3,x)

[Out]

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

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