Optimal. Leaf size=19 \[ x-\text {Int}\left (\frac {x^2}{\text {F0}(x)+x^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\text {F0}(x)}{x^2+\text {F0}(x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\text {F0}(x)}{x^2+\text {F0}(x)} \, dx &=\int \left (1-\frac {x^2}{x^2+\text {F0}(x)}\right ) \, dx\\ &=x-\int \frac {x^2}{x^2+\text {F0}(x)} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\text {F0}(x)}{x^2+\text {F0}(x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {F_{0}\relax (x)}{x^{2} + F_{0}\relax (x)}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F_{0}\relax (x)}{x^{2} + F_{0}\relax (x)}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {\mathit {F0} \relax (x )}{x^{2}+\mathit {F0} \relax (x )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F_{0}\relax (x)}{x^{2} + F_{0}\relax (x)}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {F_{0}\relax (x)}{F_{0}\relax (x)+x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {F_{0}}{\relax (x )}}{x^{2} + \operatorname {F_{0}}{\relax (x )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________