3.910 \(\int F(\frac{x^4}{(a+b x^2)^2}) \, dx\)

Optimal. Leaf size=16 \[ \text{CannotIntegrate}\left (F\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ),x\right ) \]

[Out]

CannotIntegrate[F[x^4/(a + b*x^2)^2], x]

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Rubi [A]  time = 0.0089925, 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 = {} \[ \int F\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[x^4/(a + b*x^2)^2],x]

[Out]

Defer[Int][F[x^4/(a + b*x^2)^2], x]

Rubi steps

\begin{align*} \int F\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx &=\int F\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 0.0086473, size = 0, normalized size = 0. \[ \int F\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[x^4/(a + b*x^2)^2],x]

[Out]

Integrate[F[x^4/(a + b*x^2)^2], x]

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Maple [A]  time = 0.008, size = 0, normalized size = 0. \begin{align*} \int F \left ({\frac{{x}^{4}}{ \left ( b{x}^{2}+a \right ) ^{2}}} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x^4/(b*x^2+a)^2),x)

[Out]

int(F(x^4/(b*x^2+a)^2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (\frac{x^{4}}{{\left (b x^{2} + a\right )}^{2}}\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^4/(b*x^2+a)^2),x, algorithm="maxima")

[Out]

integrate(F(x^4/(b*x^2 + a)^2), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (F\left (\frac{x^{4}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^4/(b*x^2+a)^2),x, algorithm="fricas")

[Out]

integral(F(x^4/(b^2*x^4 + 2*a*b*x^2 + a^2)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F{\left (\frac{x^{4}}{\left (a + b x^{2}\right )^{2}} \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x**4/(b*x**2+a)**2),x)

[Out]

Integral(F(x**4/(a + b*x**2)**2), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (\frac{x^{4}}{{\left (b x^{2} + a\right )}^{2}}\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x^4/(b*x^2+a)^2),x, algorithm="giac")

[Out]

integrate(F(x^4/(b*x^2 + a)^2), x)