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

Optimal. Leaf size=11 \[ \text {Int}\left (F\left (\frac {a}{x^2}+b\right ),x\right ) \]

[Out]

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

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

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*}

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

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

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

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)

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maple [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int F \left (\frac {b \,x^{2}+a}{x^{2}}\right )\, dx \]

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

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.09 \[ \int F\left (\frac {b\,x^2+a}{x^2}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F((a + b*x^2)/x^2),x)

[Out]

int(F((a + b*x^2)/x^2), x)

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

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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