Optimal. Leaf size=27 \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0285156, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{55 \log{\left (- 2 x + 1 \right )}}{4} + \int \frac{25}{4}\, dx + \frac{121}{8 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.018832, size = 26, normalized size = 0.96 \[ \frac{1}{8} \left (50 x+\frac{121}{1-2 x}+110 \log (1-2 x)-25\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 22, normalized size = 0.8 \[{\frac{25\,x}{4}}-{\frac{121}{-8+16\,x}}+{\frac{55\,\ln \left ( -1+2\,x \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.32071, size = 28, normalized size = 1.04 \[ \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} + \frac{55}{4} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(2*x - 1)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.200907, size = 43, normalized size = 1.59 \[ \frac{100 \, x^{2} + 110 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 50 \, x - 121}{8 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(2*x - 1)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.169492, size = 20, normalized size = 0.74 \[ \frac{25 x}{4} + \frac{55 \log{\left (2 x - 1 \right )}}{4} - \frac{121}{16 x - 8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209945, size = 43, normalized size = 1.59 \[ \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} - \frac{55}{4} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{25}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(2*x - 1)^2,x, algorithm="giac")
[Out]