Optimal. Leaf size=24 \[ \frac{x}{r \sqrt{-a^2-2 r (K-H r)}} \]
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Rubi [A] time = 0.0517409, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{x}{r \sqrt{-a^2-2 r (K-H r)}} \]
Antiderivative was successfully verified.
[In] Int[1/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2]),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int \frac{1}{r}\, dx}{\sqrt{2 H r^{2} - 2 K r - a^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/r/(2*H*r**2-2*K*r-a**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0000499173, size = 25, normalized size = 1.04 \[ \frac{x}{r \sqrt{-a^2+2 H r^2-2 K r}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2]),x]
[Out]
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Maple [A] time = 0.002, size = 24, normalized size = 1. \[{\frac{x}{r}{\frac{1}{\sqrt{2\,H{r}^{2}-2\,Kr-{a}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/r/(2*H*r^2-2*K*r-a^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.36765, size = 31, normalized size = 1.29 \[ \frac{x}{\sqrt{2 \, H r^{2} - a^{2} - 2 \, K r} r} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*H*r^2 - a^2 - 2*K*r)*r),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20254, size = 31, normalized size = 1.29 \[ \frac{x}{\sqrt{2 \, H r^{2} - a^{2} - 2 \, K r} r} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*H*r^2 - a^2 - 2*K*r)*r),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.037186, size = 20, normalized size = 0.83 \[ \frac{x}{r \sqrt{2 H r^{2} - 2 K r - a^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/r/(2*H*r**2-2*K*r-a**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.205796, size = 31, normalized size = 1.29 \[ \frac{x}{\sqrt{2 \, H r^{2} - a^{2} - 2 \, K r} r} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*H*r^2 - a^2 - 2*K*r)*r),x, algorithm="giac")
[Out]