Optimal. Leaf size=6 \[ -\frac{c}{x} \]
[Out]
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Rubi [A] time = 0.00592865, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087 \[ -\frac{c}{x} \]
Antiderivative was successfully verified.
[In] Int[(a*c + b*c*x^2)/(x^2*(a + b*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 3.59483, size = 3, normalized size = 0.5 \[ - \frac{c}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*c*x**2+a*c)/x**2/(b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.000589409, size = 6, normalized size = 1. \[ -\frac{c}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a*c + b*c*x^2)/(x^2*(a + b*x^2)),x]
[Out]
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Maple [A] time = 0.001, size = 7, normalized size = 1.2 \[ -{\frac{c}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*c*x^2+a*c)/x^2/(b*x^2+a),x)
[Out]
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Maxima [A] time = 1.34327, size = 8, normalized size = 1.33 \[ -\frac{c}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216027, size = 8, normalized size = 1.33 \[ -\frac{c}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.122779, size = 3, normalized size = 0.5 \[ - \frac{c}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x**2+a*c)/x**2/(b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.222543, size = 8, normalized size = 1.33 \[ -\frac{c}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x^2 + a*c)/((b*x^2 + a)*x^2),x, algorithm="giac")
[Out]