Optimal. Leaf size=19 \[ x-\text{Int}\left (\frac{x^2}{f(x)+x^2},x\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.106251, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{f(x)}{x^2+f(x)},x\right ) \]
Verification is Not applicable to the result.
[In] Int[f[x]/(x^2 + f[x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\operatorname{F_{0}}{\left (x \right )}}{x^{2} + \operatorname{F_{0}}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F0(x)/(x**2+F0(x)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0430832, size = 0, normalized size = 0. \[ \int \frac{f(x)}{x^2+f(x)} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[f[x]/(x^2 + f[x]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 0, normalized size = 0. \[ \int{\frac{f \left ( x \right ) }{{x}^{2}+f \left ( x \right ) }}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f(x)/(x^2+f(x)),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{F_{0}\left (x\right )}{x^{2} + F_{0}\left (x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F0(x)/(x^2 + F0(x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.217883, size = 5, normalized size = 0.26 \[ \text{Failed} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F0(x)/(x^2 + F0(x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\operatorname{F_{0}}{\left (x \right )}}{x^{2} + \operatorname{F_{0}}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F0(x)/(x**2+F0(x)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{F_{0}\left (x\right )}{x^{2} + F_{0}\left (x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F0(x)/(x^2 + F0(x)),x, algorithm="giac")
[Out]