3.1558 \(\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{3375 x^6}{8}+\frac{5535 x^5}{2}+\frac{557415 x^4}{64}+\frac{289951 x^3}{16}+\frac{3859469 x^2}{128}+\frac{209243 x}{4}+\frac{3195731}{256 (1-2 x)}+\frac{9836211}{256} \log (1-2 x) \]

[Out]

3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (
557415*x^4)/64 + (5535*x^5)/2 + (3375*x^6)/8 + (9836211*Log[1 - 2*x])/256

_______________________________________________________________________________________

Rubi [A]  time = 0.0809314, 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 \[ \frac{3375 x^6}{8}+\frac{5535 x^5}{2}+\frac{557415 x^4}{64}+\frac{289951 x^3}{16}+\frac{3859469 x^2}{128}+\frac{209243 x}{4}+\frac{3195731}{256 (1-2 x)}+\frac{9836211}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (
557415*x^4)/64 + (5535*x^5)/2 + (3375*x^6)/8 + (9836211*Log[1 - 2*x])/256

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{3375 x^{6}}{8} + \frac{5535 x^{5}}{2} + \frac{557415 x^{4}}{64} + \frac{289951 x^{3}}{16} + \frac{9836211 \log{\left (- 2 x + 1 \right )}}{256} + \int \frac{209243}{4}\, dx + \frac{3859469 \int x\, dx}{64} + \frac{3195731}{256 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4*(3+5*x)**3/(1-2*x)**2,x)

[Out]

3375*x**6/8 + 5535*x**5/2 + 557415*x**4/64 + 289951*x**3/16 + 9836211*log(-2*x +
1)/256 + Integral(209243/4, x) + 3859469*Integral(x, x)/64 + 3195731/(256*(-2*x
+ 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0258965, size = 59, normalized size = 0.95 \[ \frac{864000 x^7+5235840 x^6+15003360 x^5+28195088 x^4+43194640 x^3+76256664 x^2-128514958 x+39344844 (2 x-1) \log (1-2 x)[phone]}{1024 (2 x-1)} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

(24691451 - 128514958*x + 76256664*x^2 + 43194640*x^3 + 28195088*x^4 + 15003360*
x^5 + 5235840*x^6 + 864000*x^7 + 39344844*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2
*x))

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 47, normalized size = 0.8 \[{\frac{3375\,{x}^{6}}{8}}+{\frac{5535\,{x}^{5}}{2}}+{\frac{557415\,{x}^{4}}{64}}+{\frac{289951\,{x}^{3}}{16}}+{\frac{3859469\,{x}^{2}}{128}}+{\frac{209243\,x}{4}}-{\frac{3195731}{-256+512\,x}}+{\frac{9836211\,\ln \left ( -1+2\,x \right ) }{256}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x)

[Out]

3375/8*x^6+5535/2*x^5+557415/64*x^4+289951/16*x^3+3859469/128*x^2+209243/4*x-319
5731/256/(-1+2*x)+9836211/256*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33995, size = 62, normalized size = 1. \[ \frac{3375}{8} \, x^{6} + \frac{5535}{2} \, x^{5} + \frac{557415}{64} \, x^{4} + \frac{289951}{16} \, x^{3} + \frac{3859469}{128} \, x^{2} + \frac{209243}{4} \, x - \frac{3195731}{256 \,{\left (2 \, x - 1\right )}} + \frac{9836211}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^4/(2*x - 1)^2,x, algorithm="maxima")

[Out]

3375/8*x^6 + 5535/2*x^5 + 557415/64*x^4 + 289951/16*x^3 + 3859469/128*x^2 + 2092
43/4*x - 3195731/256/(2*x - 1) + 9836211/256*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.209967, size = 77, normalized size = 1.24 \[ \frac{216000 \, x^{7} + 1308960 \, x^{6} + 3750840 \, x^{5} + 7048772 \, x^{4} + 10798660 \, x^{3} + 19064166 \, x^{2} + 9836211 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 13391552 \, x - 3195731}{256 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^4/(2*x - 1)^2,x, algorithm="fricas")

[Out]

1/256*(216000*x^7 + 1308960*x^6 + 3750840*x^5 + 7048772*x^4 + 10798660*x^3 + 190
64166*x^2 + 9836211*(2*x - 1)*log(2*x - 1) - 13391552*x - 3195731)/(2*x - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.24394, size = 54, normalized size = 0.87 \[ \frac{3375 x^{6}}{8} + \frac{5535 x^{5}}{2} + \frac{557415 x^{4}}{64} + \frac{289951 x^{3}}{16} + \frac{3859469 x^{2}}{128} + \frac{209243 x}{4} + \frac{9836211 \log{\left (2 x - 1 \right )}}{256} - \frac{3195731}{512 x - 256} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4*(3+5*x)**3/(1-2*x)**2,x)

[Out]

3375*x**6/8 + 5535*x**5/2 + 557415*x**4/64 + 289951*x**3/16 + 3859469*x**2/128 +
209243*x/4 + 9836211*log(2*x - 1)/256 - 3195731/(512*x - 256)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.214006, size = 113, normalized size = 1.82 \[ \frac{1}{1024} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{129060}{2 \, x - 1} + \frac{1101465}{{\left (2 \, x - 1\right )}^{2}} + \frac{5569868}{{\left (2 \, x - 1\right )}^{3}} + \frac{19009102}{{\left (2 \, x - 1\right )}^{4}} + \frac{51892764}{{\left (2 \, x - 1\right )}^{5}} + 6750\right )} - \frac{3195731}{256 \,{\left (2 \, x - 1\right )}} - \frac{9836211}{256} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^4/(2*x - 1)^2,x, algorithm="giac")

[Out]

1/1024*(2*x - 1)^6*(129060/(2*x - 1) + 1101465/(2*x - 1)^2 + 5569868/(2*x - 1)^3
+ 19009102/(2*x - 1)^4 + 51892764/(2*x - 1)^5 + 6750) - 3195731/256/(2*x - 1) -
9836211/256*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)