Optimal. Leaf size=16 \[ x \log \left (x^2+1\right )-2 x+2 \tan ^{-1}(x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0143375, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x \log \left (x^2+1\right )-2 x+2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[Log[1 + x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.61095, size = 15, normalized size = 0.94 \[ x \log{\left (x^{2} + 1 \right )} - 2 x + 2 \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(x**2+1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0038302, size = 16, normalized size = 1. \[ x \log \left (x^2+1\right )-2 x+2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[Log[1 + x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 17, normalized size = 1.1 \[ -2\,x+2\,\arctan \left ( x \right ) +x\ln \left ({x}^{2}+1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(x^2+1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.51649, size = 22, normalized size = 1.38 \[ x \log \left (x^{2} + 1\right ) - 2 \, x + 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x^2 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208972, size = 22, normalized size = 1.38 \[ x \log \left (x^{2} + 1\right ) - 2 \, x + 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x^2 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.127364, size = 15, normalized size = 0.94 \[ x \log{\left (x^{2} + 1 \right )} - 2 x + 2 \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(x**2+1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.202274, size = 22, normalized size = 1.38 \[ x{\rm ln}\left (x^{2} + 1\right ) - 2 \, x + 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x^2 + 1),x, algorithm="giac")
[Out]