Optimal. Leaf size=32 \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0434601, antiderivative size = 32, 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 \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.68426, size = 24, normalized size = 0.75 \[ \frac{407 \log{\left (- 2 x + 1 \right )}}{196} + \frac{\log{\left (3 x + 2 \right )}}{147} + \frac{121}{28 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**2/(2+3*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0249334, size = 40, normalized size = 1.25 \[ -\frac{363}{28 (2 (3 x+2)-7)}+\frac{1}{147} \log (3 x+2)+\frac{407}{196} \log (7-2 (3 x+2)) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 27, normalized size = 0.8 \[{\frac{\ln \left ( 2+3\,x \right ) }{147}}-{\frac{121}{-28+56\,x}}+{\frac{407\,\ln \left ( -1+2\,x \right ) }{196}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^2/(2+3*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33838, size = 35, normalized size = 1.09 \[ -\frac{121}{28 \,{\left (2 \, x - 1\right )}} + \frac{1}{147} \, \log \left (3 \, x + 2\right ) + \frac{407}{196} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)*(2*x - 1)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210355, size = 50, normalized size = 1.56 \[ \frac{4 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 1221 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2541}{588 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)*(2*x - 1)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.309411, size = 24, normalized size = 0.75 \[ \frac{407 \log{\left (x - \frac{1}{2} \right )}}{196} + \frac{\log{\left (x + \frac{2}{3} \right )}}{147} - \frac{121}{56 x - 28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**2/(2+3*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.207518, size = 58, normalized size = 1.81 \[ -\frac{121}{28 \,{\left (2 \, x - 1\right )}} - \frac{25}{12} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{147} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)*(2*x - 1)^2),x, algorithm="giac")
[Out]