3.766 \(\int f\left (\frac{x^2}{a+b x^2}\right ) \, dx\)

Optimal. Leaf size=17 \[ \text{Int}\left (f\left (\frac{x^2}{a+b x^2}\right ),x\right ) \]

[Out]

CannotIntegrate[f[x^2/(a + b*x^2)], x]

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Rubi [A]  time = 0.0169517, 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. \[ \text{Int}\left (f\left (\frac{x^2}{a+b x^2}\right ),x\right ) \]

Verification is Not applicable to the result.

[In]  Int[f[x^2/(a + b*x^2)],x]

[Out]

Defer[Int][f[x^2/(a + b*x^2)], x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int F{\left (\frac{x^{2}}{a + b x^{2}} \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(F(x**2/(b*x**2+a)),x)

[Out]

Integral(F(x**2/(a + b*x**2)), x)

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Mathematica [A]  time = 0.00849107, size = 0, normalized size = 0. \[ \int f\left (\frac{x^2}{a+b x^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[f[x^2/(a + b*x^2)],x]

[Out]

Integrate[f[x^2/(a + b*x^2)], x]

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Maple [A]  time = 0., size = 0, normalized size = 0. \[ \int f \left ({\frac{{x}^{2}}{b{x}^{2}+a}} \right ) \, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f(x^2/(b*x^2+a)),x)

[Out]

int(f(x^2/(b*x^2+a)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int F\left (\frac{x^{2}}{b x^{2} + a}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x^2/(b*x^2 + a)),x, algorithm="maxima")

[Out]

integrate(F(x^2/(b*x^2 + a)), x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x^2/(b*x^2 + a)),x, algorithm="fricas")

[Out]

Exception raised: TypeError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int F{\left (\frac{x^{2}}{a + b x^{2}} \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x**2/(b*x**2+a)),x)

[Out]

Integral(F(x**2/(a + b*x**2)), x)

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int F\left (\frac{x^{2}}{b x^{2} + a}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x^2/(b*x^2 + a)),x, algorithm="giac")

[Out]

integrate(F(x^2/(b*x^2 + a)), x)