Optimal. Leaf size=27 \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0257625, 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 \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{44 \log{\left (5 x + 3 \right )}}{125} + \int \frac{4}{25}\, dx - \frac{121}{125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0161537, size = 34, normalized size = 1.26 \[ \frac{100 x^2+10 x-44 (5 x+3) \log (10 x+6)-151}{125 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 22, normalized size = 0.8 \[{\frac{4\,x}{25}}-{\frac{121}{375+625\,x}}-{\frac{44\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33502, size = 28, normalized size = 1.04 \[ \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} - \frac{44}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.206866, size = 43, normalized size = 1.59 \[ \frac{100 \, x^{2} - 44 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 60 \, x - 121}{125 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.186128, size = 20, normalized size = 0.74 \[ \frac{4 x}{25} - \frac{44 \log{\left (5 x + 3 \right )}}{125} - \frac{121}{625 x + 375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.233796, size = 43, normalized size = 1.59 \[ \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} + \frac{44}{125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{12}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")
[Out]