Optimal. Leaf size=18 \[ \frac{\sqrt{16 x^2-9}}{9 x} \]
[Out]
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Rubi [A] time = 0.0136649, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\sqrt{16 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*Sqrt[-9 + 16*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 1.40988, size = 12, normalized size = 0.67 \[ \frac{\sqrt{16 x^{2} - 9}}{9 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(16*x**2-9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00983276, size = 18, normalized size = 1. \[ \frac{\sqrt{16 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*Sqrt[-9 + 16*x^2]),x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 1.4 \[{\frac{ \left ( 4\,x-3 \right ) \left ( 3+4\,x \right ) }{9\,x}{\frac{1}{\sqrt{16\,{x}^{2}-9}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(16*x^2-9)^(1/2),x)
[Out]
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Maxima [A] time = 1.49915, size = 19, normalized size = 1.06 \[ \frac{\sqrt{16 \, x^{2} - 9}}{9 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(16*x^2 - 9)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202311, size = 27, normalized size = 1.5 \[ \frac{1}{4 \, x^{2} - \sqrt{16 \, x^{2} - 9} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(16*x^2 - 9)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.27853, size = 39, normalized size = 2.17 \[ \begin{cases} \frac{4 i \sqrt{-1 + \frac{9}{16 x^{2}}}}{9} & \text{for}\: \frac{9 \left |{\frac{1}{x^{2}}}\right |}{16} > 1 \\\frac{4 \sqrt{1 - \frac{9}{16 x^{2}}}}{9} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(16*x**2-9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.208524, size = 31, normalized size = 1.72 \[ \frac{8}{{\left (4 \, x - \sqrt{16 \, x^{2} - 9}\right )}^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(16*x^2 - 9)*x^2),x, algorithm="giac")
[Out]