Optimal. Leaf size=13 \[ \frac{1}{b \left (a+\frac{b}{x}\right )} \]
[Out]
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Rubi [A] time = 0.0169857, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{b \left (a+\frac{b}{x}\right )} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.25561, size = 7, normalized size = 0.54 \[ \frac{1}{b \left (a + \frac{b}{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**2/x**2,x)
[Out]
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Mathematica [A] time = 0.00548419, size = 12, normalized size = 0.92 \[ -\frac{1}{a (a x+b)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^2*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 13, normalized size = 1. \[ -{\frac{1}{ \left ( ax+b \right ) a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^2/x^2,x)
[Out]
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Maxima [A] time = 1.42094, size = 18, normalized size = 1.38 \[ \frac{1}{{\left (a + \frac{b}{x}\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211075, size = 18, normalized size = 1.38 \[ -\frac{1}{a^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.11713, size = 10, normalized size = 0.77 \[ - \frac{1}{a^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**2/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.222367, size = 18, normalized size = 1.38 \[ \frac{1}{{\left (a + \frac{b}{x}\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^2),x, algorithm="giac")
[Out]