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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.01, 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 = {} \[ \int F\left (\frac {x^2}{a+b x^2}\right ) \, dx \]

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 = 0.01, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^2}{a+b x^2}\right ) \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (\frac {x^{2}}{b x^{2} + a}\right ), x\right ) \]

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)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^{2}}{b x^{2} + a}\right )\,{d x} \]

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)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int F \left (\frac {x^{2}}{b \,x^{2}+a}\right )\, dx \]

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)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {x^{2}}{b x^{2} + a}\right )\,{d x} \]

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)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int F\left (\frac {x^2}{b\,x^2+a}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x^2/(a + b*x^2)),x)

[Out]

int(F(x^2/(a + b*x^2)), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F{\left (\frac {x^{2}}{a + b x^{2}} \right )}\, dx \]

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)

________________________________________________________________________________________