3.746 \(\int \frac{f(x)}{x^2+f(x)} \, dx\)

Optimal. Leaf size=19 \[ x-\text{Int}\left (\frac{x^2}{f(x)+x^2},x\right ) \]

[Out]

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

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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]

x - Defer[Int][x^2/(x^2 + f[x]), x]

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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]

Integral(F0(x)/(x**2 + F0(x)), x)

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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]

Integrate[f[x]/(x^2 + f[x]), x]

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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]

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

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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]

integrate(F0(x)/(x^2 + F0(x)), x)

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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]

Failed

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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]

Integral(F0(x)/(x**2 + F0(x)), x)

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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]

integrate(F0(x)/(x^2 + F0(x)), x)