3.763 \(\int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx\)

Optimal. Leaf size=18 \[ x-\text{CannotIntegrate}\left (\frac{x^2}{\text{F0}(x)+x^2},x\right ) \]

[Out]

x - CannotIntegrate[x^2/(x^2 + F0[x]), x]

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Rubi [A]  time = 0.0699767, 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., Rules used = {} \[ \int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[F0[x]/(x^2 + F0[x]),x]

[Out]

x - Defer[Int][x^2/(x^2 + F0[x]), x]

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 = 0.0439654, size = 0, normalized size = 0. \[ \int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F0[x]/(x^2 + F0[x]),x]

[Out]

Integrate[F0[x]/(x^2 + F0[x]), x]

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Maple [A]  time = 0.021, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it F0} \left ( x \right ) }{{x}^{2}+{\it F0} \left ( x \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F0(x)/(x^2+F0(x)),x)

[Out]

int(F0(x)/(x^2+F0(x)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F_{0}\left (x\right )}{x^{2} + F_{0}\left (x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F0(x)/(x^2+F0(x)),x, algorithm="maxima")

[Out]

integrate(F0(x)/(x^2 + F0(x)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{F_{0}\left (x\right )}{x^{2} + F_{0}\left (x\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F0(x)/(x^2+F0(x)),x, algorithm="fricas")

[Out]

integral(F0(x)/(x^2 + F0(x)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{F_{0}}{\left (x \right )}}{x^{2} + \operatorname{F_{0}}{\left (x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F0(x)/(x**2+F0(x)),x)

[Out]

Integral(F0(x)/(x**2 + F0(x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F_{0}\left (x\right )}{x^{2} + F_{0}\left (x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F0(x)/(x^2+F0(x)),x, algorithm="giac")

[Out]

integrate(F0(x)/(x^2 + F0(x)), x)