Optimal. Leaf size=25 \[ \frac{1}{2} \log \left (1-x^2\right )+\frac{3}{2} \log \left (4-x^2\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0506523, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{1}{2} \log \left (1-x^2\right )+\frac{3}{2} \log \left (4-x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(x*(-7 + 4*x^2))/(4 - 5*x^2 + x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.855, size = 17, normalized size = 0.68 \[ \frac{\log{\left (- x^{2} + 1 \right )}}{2} + \frac{3 \log{\left (- x^{2} + 4 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(4*x**2-7)/(x**4-5*x**2+4),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00999147, size = 25, normalized size = 1. \[ \frac{1}{2} \log \left (1-x^2\right )+\frac{3}{2} \log \left (4-x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(x*(-7 + 4*x^2))/(4 - 5*x^2 + x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 18, normalized size = 0.7 \[{\frac{\ln \left ({x}^{2}-1 \right ) }{2}}+{\frac{3\,\ln \left ({x}^{2}-4 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(4*x^2-7)/(x^4-5*x^2+4),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.701921, size = 23, normalized size = 0.92 \[ \frac{1}{2} \, \log \left (x^{2} - 1\right ) + \frac{3}{2} \, \log \left (x^{2} - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 - 7)*x/(x^4 - 5*x^2 + 4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.253026, size = 23, normalized size = 0.92 \[ \frac{1}{2} \, \log \left (x^{2} - 1\right ) + \frac{3}{2} \, \log \left (x^{2} - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 - 7)*x/(x^4 - 5*x^2 + 4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.231747, size = 17, normalized size = 0.68 \[ \frac{3 \log{\left (x^{2} - 4 \right )}}{2} + \frac{\log{\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(4*x**2-7)/(x**4-5*x**2+4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.289875, size = 26, normalized size = 1.04 \[ \frac{1}{2} \,{\rm ln}\left ({\left | x^{2} - 1 \right |}\right ) + \frac{3}{2} \,{\rm ln}\left ({\left | x^{2} - 4 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 - 7)*x/(x^4 - 5*x^2 + 4),x, algorithm="giac")
[Out]