Optimal. Leaf size=12 \[ \frac{x}{a-b x^2} \]
[Out]
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Rubi [A] time = 0.00976524, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{x}{a-b x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)/(-a + b*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 6.7902, size = 7, normalized size = 0.58 \[ \frac{x}{a - b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)/(b*x**2-a)**2,x)
[Out]
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Mathematica [A] time = 0.0115159, size = 14, normalized size = 1.17 \[ -\frac{x}{b x^2-a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)/(-a + b*x^2)^2,x]
[Out]
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Maple [A] time = 0.009, size = 15, normalized size = 1.3 \[ -{\frac{x}{b{x}^{2}-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)/(b*x^2-a)^2,x)
[Out]
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Maxima [A] time = 1.34745, size = 19, normalized size = 1.58 \[ -\frac{x}{b x^{2} - a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/(b*x^2 - a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223489, size = 19, normalized size = 1.58 \[ -\frac{x}{b x^{2} - a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/(b*x^2 - a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.29411, size = 8, normalized size = 0.67 \[ - \frac{x}{- a + b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)/(b*x**2-a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.228688, size = 19, normalized size = 1.58 \[ -\frac{x}{b x^{2} - a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/(b*x^2 - a)^2,x, algorithm="giac")
[Out]