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

Optimal. Leaf size=10 \[ \text{CannotIntegrate}\left (F\left (\frac{a}{x^2}+b\right ),x\right ) \]

[Out]

CannotIntegrate[F[b + a/x^2], x]

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Rubi [A]  time = 0.0126367, 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 = {} \[ \int F\left (\frac{a+b x^2}{x^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[(a + b*x^2)/x^2],x]

[Out]

Defer[Int][F[b + a/x^2], x]

Rubi steps

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

Mathematica [A]  time = 0.0053383, size = 0, normalized size = 0. \[ \int F\left (\frac{a+b x^2}{x^2}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[(a + b*x^2)/x^2],x]

[Out]

Integrate[F[(a + b*x^2)/x^2], x]

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Maple [A]  time = 0.007, size = 0, normalized size = 0. \begin{align*} \int F \left ({\frac{b{x}^{2}+a}{{x}^{2}}} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F((b*x^2 + a)/x^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(F((b*x^2 + a)/x^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(F((a + b*x**2)/x**2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F((b*x^2 + a)/x^2), x)