Optimal. Leaf size=10 \[ -\frac{1}{x (a+b)} \]
[Out]
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Rubi [A] time = 0.00727225, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{1}{x (a+b)} \]
Antiderivative was successfully verified.
[In] Int[(a*x^2 + b*x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 2.29567, size = 7, normalized size = 0.7 \[ - \frac{1}{x \left (a + b\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a*x**2+b*x**2),x)
[Out]
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Mathematica [A] time = 0.00131545, size = 10, normalized size = 1. \[ -\frac{1}{x (a+b)} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^2 + b*x^2)^(-1),x]
[Out]
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Maple [A] time = 0.001, size = 11, normalized size = 1.1 \[ -{\frac{1}{ \left ( a+b \right ) x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a*x^2+b*x^2),x)
[Out]
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Maxima [A] time = 1.39618, size = 14, normalized size = 1.4 \[ -\frac{1}{{\left (a + b\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^2 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200741, size = 14, normalized size = 1.4 \[ -\frac{1}{{\left (a + b\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^2 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.095939, size = 7, normalized size = 0.7 \[ - \frac{1}{x \left (a + b\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x**2+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.217472, size = 14, normalized size = 1.4 \[ -\frac{1}{{\left (a + b\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^2 + b*x^2),x, algorithm="giac")
[Out]