3.1615 \(\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^3} \, dx\)

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 - (44469*x^4)/64 - (729*x^5)/8 - (5078115*Log[1 - 2*x])/
256

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Rubi [A]  time = 0.0823787, 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 \[ -\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x) \]

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 - (44469*x^4)/64 - (729*x^5)/8 - (5078115*Log[1 - 2*x])/
256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{5}}{8} - \frac{44469 x^{4}}{64} - \frac{10611 x^{3}}{4} - \frac{5078115 \log{\left (- 2 x + 1 \right )}}{256} + \int \left (- \frac{2431647}{128}\right )\, dx - \frac{461835 \int x\, dx}{32} - \frac{3916031}{256 \left (- 2 x + 1\right )} + \frac{1294139}{512 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_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 - 5078115*log(-2*x + 1)/256 + Integra
l(-2431647/128, x) - 461835*Integral(x, x)/32 - 3916031/(256*(-2*x + 1)) + 12941
39/(512*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0284778, 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 = 0.01, size = 51, normalized size = 0.8 \[ -{\frac{729\,{x}^{5}}{8}}-{\frac{44469\,{x}^{4}}{64}}-{\frac{10611\,{x}^{3}}{4}}-{\frac{461835\,{x}^{2}}{64}}-{\frac{2431647\,x}{128}}+{\frac{1294139}{512\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{3916031}{-256+512\,x}}-{\frac{5078115\,\ln \left ( -1+2\,x \right ) }{256}} \]

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+1294139/512/(-1+
2*x)^2+3916031/256/(-1+2*x)-5078115/256*ln(-1+2*x)

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Maxima [A]  time = 1.35347, size = 69, normalized size = 1.05 \[ -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{5078115}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^6/(2*x - 1)^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 = 0.213666, size = 90, normalized size = 1.36 \[ -\frac{186624 \, x^{7} + 1236384 \, x^{6} + 4056480 \, x^{5} + 9701640 \, x^{4} + 25485840 \, x^{3} - 35211672 \, x^{2} + 10156230 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 5937536 \, x + 6537923}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/512*(186624*x^7 + 1236384*x^6 + 4056480*x^5 + 9701640*x^4 + 25485840*x^3 - 35
211672*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 = 0.313377, size = 56, normalized size = 0.85 \[ - \frac{729 x^{5}}{8} - \frac{44469 x^{4}}{64} - \frac{10611 x^{3}}{4} - \frac{461835 x^{2}}{64} - \frac{2431647 x}{128} + \frac{15664124 x - 6537923}{2048 x^{2} - 2048 x + 512} - \frac{5078115 \log{\left (2 x - 1 \right )}}{256} \]

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 + (1
5664124*x - 6537923)/(2048*x**2 - 2048*x + 512) - 5078115*log(2*x - 1)/256

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GIAC/XCAS [A]  time = 0.207185, size = 63, normalized size = 0.95 \[ -\frac{729}{8} \, x^{5} - \frac{44469}{64} \, x^{4} - \frac{10611}{4} \, x^{3} - \frac{461835}{64} \, x^{2} - \frac{2431647}{128} \, x + \frac{16807 \,{\left (932 \, x - 389\right )}}{512 \,{\left (2 \, x - 1\right )}^{2}} - \frac{5078115}{256} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^6/(2*x - 1)^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*ln(abs(2*x - 1))