3.1419 \(\int \frac{(2+3 x)^6 (3+5 x)}{1-2 x} \, dx\)

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 - (1693
71*x^5)/40 - (12393*x^6)/8 - (3645*x^7)/14 - (1294139*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0504396, 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 \[ -\frac{3645 x^7}{14}-\frac{12393 x^6}{8}-\frac{169371 x^5}{40}-\frac{458811 x^4}{64}-\frac{279657 x^3}{32}-\frac{1138491 x^2}{128}-\frac{1269563 x}{128}-\frac{1294139}{256} \log (1-2 x) \]

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 - (1693
71*x^5)/40 - (12393*x^6)/8 - (3645*x^7)/14 - (1294139*Log[1 - 2*x])/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{3645 x^{7}}{14} - \frac{12393 x^{6}}{8} - \frac{169371 x^{5}}{40} - \frac{458811 x^{4}}{64} - \frac{279657 x^{3}}{32} - \frac{1294139 \log{\left (- 2 x + 1 \right )}}{256} + \int \left (- \frac{1269563}{128}\right )\, dx - \frac{1138491 \int x\, dx}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_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
- 1294139*log(-2*x + 1)/256 + Integral(-1269563/128, x) - 1138491*Integral(x, x)
/64

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Mathematica [A]  time = 0.0236336, 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 - 15175
6416*x^5 - 55520640*x^6 - 9331200*x^7 - 181179460*Log[1 - 2*x])/35840

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Maple [A]  time = 0.006, size = 43, normalized size = 0.7 \[ -{\frac{3645\,{x}^{7}}{14}}-{\frac{12393\,{x}^{6}}{8}}-{\frac{169371\,{x}^{5}}{40}}-{\frac{458811\,{x}^{4}}{64}}-{\frac{279657\,{x}^{3}}{32}}-{\frac{1138491\,{x}^{2}}{128}}-{\frac{1269563\,x}{128}}-{\frac{1294139\,\ln \left ( -1+2\,x \right ) }{256}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

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Maxima [A]  time = 1.34351, size = 57, normalized size = 0.98 \[ -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 113
8491/128*x^2 - 1269563/128*x - 1294139/256*log(2*x - 1)

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Fricas [A]  time = 0.208387, size = 57, normalized size = 0.98 \[ -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 113
8491/128*x^2 - 1269563/128*x - 1294139/256*log(2*x - 1)

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Sympy [A]  time = 0.198737, size = 56, normalized size = 0.97 \[ - \frac{3645 x^{7}}{14} - \frac{12393 x^{6}}{8} - \frac{169371 x^{5}}{40} - \frac{458811 x^{4}}{64} - \frac{279657 x^{3}}{32} - \frac{1138491 x^{2}}{128} - \frac{1269563 x}{128} - \frac{1294139 \log{\left (2 x - 1 \right )}}{256} \]

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/XCAS [A]  time = 0.209243, size = 58, normalized size = 1. \[ -\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 113
8491/128*x^2 - 1269563/128*x - 1294139/256*ln(abs(2*x - 1))