3.764 \(\int f\left (\frac{a+b x^2}{x^2}\right ) \, dx\)

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 = 0.0220187, 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. \[ \text{Int}\left (f\left (\frac{a+b x^2}{x^2}\right ),x\right ) \]

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]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(F((b*x**2+a)/x**2),x)

[Out]

Integral(F(a/x**2 + b), x)

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Mathematica [A]  time = 0.00567234, 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 = 0.008, size = 0, normalized size = 0. \[ \int f \left ({\frac{b{x}^{2}+a}{{x}^{2}}} \right ) \, dx \]

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

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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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: TypeError

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

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

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)