3.1541 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]

[Out]

290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*
x^4)/16 + (405*x^5)/4 + (381073*Log[1 - 2*x])/64

_______________________________________________________________________________________

Rubi [A]  time = 0.0723782, antiderivative size = 55, 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 \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*
x^4)/16 + (405*x^5)/4 + (381073*Log[1 - 2*x])/64

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{405 x^{5}}{4} + \frac{9855 x^{4}}{16} + \frac{29277 x^{3}}{16} + \frac{381073 \log{\left (- 2 x + 1 \right )}}{64} + \int \frac{480841}{64}\, dx + \frac{15159 \int x\, dx}{2} + \frac{290521}{128 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405*x**5/4 + 9855*x**4/16 + 29277*x**3/16 + 381073*log(-2*x + 1)/64 + Integral(4
80841/64, x) + 15159*Integral(x, x)/2 + 290521/(128*(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0309692, size = 54, normalized size = 0.98 \[ \frac{51840 x^6+289440 x^5+779184 x^4+1471920 x^3+2876552 x^2-4470254 x+1524292 (2 x-1) \log (1-2 x)+692403}{256 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(692403 - 4470254*x + 2876552*x^2 + 1471920*x^3 + 779184*x^4 + 289440*x^5 + 5184
0*x^6 + 1524292*(-1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))

_______________________________________________________________________________________

Maple [A]  time = 0.011, size = 42, normalized size = 0.8 \[{\frac{405\,{x}^{5}}{4}}+{\frac{9855\,{x}^{4}}{16}}+{\frac{29277\,{x}^{3}}{16}}+{\frac{15159\,{x}^{2}}{4}}+{\frac{480841\,x}{64}}-{\frac{290521}{-128+256\,x}}+{\frac{381073\,\ln \left ( -1+2\,x \right ) }{64}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405/4*x^5+9855/16*x^4+29277/16*x^3+15159/4*x^2+480841/64*x-290521/128/(-1+2*x)+3
81073/64*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.35844, size = 55, normalized size = 1. \[ \frac{405}{4} \, x^{5} + \frac{9855}{16} \, x^{4} + \frac{29277}{16} \, x^{3} + \frac{15159}{4} \, x^{2} + \frac{480841}{64} \, x - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} + \frac{381073}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405/4*x^5 + 9855/16*x^4 + 29277/16*x^3 + 15159/4*x^2 + 480841/64*x - 290521/128/
(2*x - 1) + 381073/64*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.209972, size = 70, normalized size = 1.27 \[ \frac{25920 \, x^{6} + 144720 \, x^{5} + 389592 \, x^{4} + 735960 \, x^{3} + 1438276 \, x^{2} + 762146 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 961682 \, x - 290521}{128 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/128*(25920*x^6 + 144720*x^5 + 389592*x^4 + 735960*x^3 + 1438276*x^2 + 762146*(
2*x - 1)*log(2*x - 1) - 961682*x - 290521)/(2*x - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.230216, size = 48, normalized size = 0.87 \[ \frac{405 x^{5}}{4} + \frac{9855 x^{4}}{16} + \frac{29277 x^{3}}{16} + \frac{15159 x^{2}}{4} + \frac{480841 x}{64} + \frac{381073 \log{\left (2 x - 1 \right )}}{64} - \frac{290521}{256 x - 128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405*x**5/4 + 9855*x**4/16 + 29277*x**3/16 + 15159*x**2/4 + 480841*x/64 + 381073*
log(2*x - 1)/64 - 290521/(256*x - 128)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.212503, size = 101, normalized size = 1.84 \[ \frac{1}{256} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{13905}{2 \, x - 1} + \frac{106074}{{\left (2 \, x - 1\right )}^{2}} + \frac{485436}{{\left (2 \, x - 1\right )}^{3}} + \frac{1665902}{{\left (2 \, x - 1\right )}^{4}} + 810\right )} - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} - \frac{381073}{64} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/256*(2*x - 1)^5*(13905/(2*x - 1) + 106074/(2*x - 1)^2 + 485436/(2*x - 1)^3 + 1
665902/(2*x - 1)^4 + 810) - 290521/128/(2*x - 1) - 381073/64*ln(1/2*abs(2*x - 1)
/(2*x - 1)^2)