3.908 \(\int F(\frac{x^2}{a+b x^2}) \, dx\)

Optimal. Leaf size=16 \[ \text{CannotIntegrate}\left (F\left (\frac{x^2}{a+b x^2}\right ),x\right ) \]

[Out]

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

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Rubi [A]  time = 0.008748, 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 = {} \[ \int F\left (\frac{x^2}{a+b x^2}\right ) \, dx \]

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]

Rubi steps

\begin{align*} \int F\left (\frac{x^2}{a+b x^2}\right ) \, dx &=\int F\left (\frac{x^2}{a+b x^2}\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 0.0064459, 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 = 0.005, size = 0, normalized size = 0. \begin{align*} \int F \left ({\frac{{x}^{2}}{b{x}^{2}+a}} \right ) \, dx \end{align*}

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. \begin{align*} \int F\left (\frac{x^{2}}{b x^{2} + a}\right )\,{d x} \end{align*}

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(F(x^2/(b*x^2 + a)), x)

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

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

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)