3.1540 \(\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{2025 x^6}{8}+\frac{6723 x^5}{4}+\frac{342333 x^4}{64}+\frac{89913 x^3}{8}+\frac{2412699 x^2}{128}+\frac{2104901 x}{64}+\frac{2033647}{256 (1-2 x)}+\frac{6206585}{256} \log (1-2 x) \]

[Out]

2033647/(256*(1 - 2*x)) + (2104901*x)/64 + (2412699*x^2)/128 + (89913*x^3)/8 + (
342333*x^4)/64 + (6723*x^5)/4 + (2025*x^6)/8 + (6206585*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0802287, antiderivative size = 62, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{2025 x^6}{8}+\frac{6723 x^5}{4}+\frac{342333 x^4}{64}+\frac{89913 x^3}{8}+\frac{2412699 x^2}{128}+\frac{2104901 x}{64}+\frac{2033647}{256 (1-2 x)}+\frac{6206585}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

2033647/(256*(1 - 2*x)) + (2104901*x)/64 + (2412699*x^2)/128 + (89913*x^3)/8 + (
342333*x^4)/64 + (6723*x^5)/4 + (2025*x^6)/8 + (6206585*Log[1 - 2*x])/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{2025 x^{6}}{8} + \frac{6723 x^{5}}{4} + \frac{342333 x^{4}}{64} + \frac{89913 x^{3}}{8} + \frac{6206585 \log{\left (- 2 x + 1 \right )}}{256} + \int \frac{2104901}{64}\, dx + \frac{2412699 \int x\, dx}{64} + \frac{2033647}{256 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**5*(3+5*x)**2/(1-2*x)**2,x)

[Out]

2025*x**6/8 + 6723*x**5/4 + 342333*x**4/64 + 89913*x**3/8 + 6206585*log(-2*x + 1
)/256 + Integral(2104901/64, x) + 2412699*Integral(x, x)/64 + 2033647/(256*(-2*x
+ 1))

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Mathematica [A]  time = 0.0268645, size = 59, normalized size = 0.95 \[ \frac{518400 x^7+3182976 x^6+9233568 x^5+17540400 x^4+27094320 x^3+48055240 x^2-80685178 x+24826340 (2 x-1) \log (1-2 x)[phone]}{1024 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(15368793 - 80685178*x + 48055240*x^2 + 27094320*x^3 + 17540400*x^4 + 9233568*x^
5 + 3182976*x^6 + 518400*x^7 + 24826340*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x
))

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Maple [A]  time = 0.009, size = 47, normalized size = 0.8 \[{\frac{2025\,{x}^{6}}{8}}+{\frac{6723\,{x}^{5}}{4}}+{\frac{342333\,{x}^{4}}{64}}+{\frac{89913\,{x}^{3}}{8}}+{\frac{2412699\,{x}^{2}}{128}}+{\frac{2104901\,x}{64}}-{\frac{2033647}{-256+512\,x}}+{\frac{6206585\,\ln \left ( -1+2\,x \right ) }{256}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2025/8*x^6+6723/4*x^5+342333/64*x^4+89913/8*x^3+2412699/128*x^2+2104901/64*x-203
3647/256/(-1+2*x)+6206585/256*ln(-1+2*x)

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Maxima [A]  time = 1.35311, size = 62, normalized size = 1. \[ \frac{2025}{8} \, x^{6} + \frac{6723}{4} \, x^{5} + \frac{342333}{64} \, x^{4} + \frac{89913}{8} \, x^{3} + \frac{2412699}{128} \, x^{2} + \frac{2104901}{64} \, x - \frac{2033647}{256 \,{\left (2 \, x - 1\right )}} + \frac{6206585}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2025/8*x^6 + 6723/4*x^5 + 342333/64*x^4 + 89913/8*x^3 + 2412699/128*x^2 + 210490
1/64*x - 2033647/256/(2*x - 1) + 6206585/256*log(2*x - 1)

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Fricas [A]  time = 0.218673, size = 77, normalized size = 1.24 \[ \frac{129600 \, x^{7} + 795744 \, x^{6} + 2308392 \, x^{5} + 4385100 \, x^{4} + 6773580 \, x^{3} + 12013810 \, x^{2} + 6206585 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 8419604 \, x - 2033647}{256 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/256*(129600*x^7 + 795744*x^6 + 2308392*x^5 + 4385100*x^4 + 6773580*x^3 + 12013
810*x^2 + 6206585*(2*x - 1)*log(2*x - 1) - 8419604*x - 2033647)/(2*x - 1)

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Sympy [A]  time = 0.247278, size = 54, normalized size = 0.87 \[ \frac{2025 x^{6}}{8} + \frac{6723 x^{5}}{4} + \frac{342333 x^{4}}{64} + \frac{89913 x^{3}}{8} + \frac{2412699 x^{2}}{128} + \frac{2104901 x}{64} + \frac{6206585 \log{\left (2 x - 1 \right )}}{256} - \frac{2033647}{512 x - 256} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**5*(3+5*x)**2/(1-2*x)**2,x)

[Out]

2025*x**6/8 + 6723*x**5/4 + 342333*x**4/64 + 89913*x**3/8 + 2412699*x**2/128 + 2
104901*x/64 + 6206585*log(2*x - 1)/256 - 2033647/(512*x - 256)

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GIAC/XCAS [A]  time = 0.216083, size = 113, normalized size = 1.82 \[ \frac{1}{1024} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{78084}{2 \, x - 1} + \frac{672003}{{\left (2 \, x - 1\right )}^{2}} + \frac{3426780}{{\left (2 \, x - 1\right )}^{3}} + \frac{11793810}{{\left (2 \, x - 1\right )}^{4}} + \frac{32468380}{{\left (2 \, x - 1\right )}^{5}} + 4050\right )} - \frac{2033647}{256 \,{\left (2 \, x - 1\right )}} - \frac{6206585}{256} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1024*(2*x - 1)^6*(78084/(2*x - 1) + 672003/(2*x - 1)^2 + 3426780/(2*x - 1)^3 +
11793810/(2*x - 1)^4 + 32468380/(2*x - 1)^5 + 4050) - 2033647/256/(2*x - 1) - 6
206585/256*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)