Optimal. Leaf size=19 \[ 2 \sqrt{\sqrt{a^2+x^2}+x} \]
[Out]
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Rubi [A] time = 0.10589, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069 \[ 2 \sqrt{\sqrt{a^2+x^2}+x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a^2 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 3.64378, size = 15, normalized size = 0.79 \[ 2 \sqrt{x + \sqrt{a^{2} + x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+(a**2+x**2)**(1/2))**(1/2)/(a**2+x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0264594, size = 19, normalized size = 1. \[ 2 \sqrt{\sqrt{a^2+x^2}+x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x + Sqrt[a^2 + x^2]]/Sqrt[a^2 + x^2],x]
[Out]
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Maple [F] time = 0.039, size = 0, normalized size = 0. \[ \int{1\sqrt{x+\sqrt{{a}^{2}+{x}^{2}}}{\frac{1}{\sqrt{{a}^{2}+{x}^{2}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+(a^2+x^2)^(1/2))^(1/2)/(a^2+x^2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x + \sqrt{a^{2} + x^{2}}}}{\sqrt{a^{2} + x^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + sqrt(a^2 + x^2))/sqrt(a^2 + x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218391, size = 20, normalized size = 1.05 \[ 2 \, \sqrt{x + \sqrt{a^{2} + x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + sqrt(a^2 + x^2))/sqrt(a^2 + x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.282316, size = 15, normalized size = 0.79 \[ 2 \sqrt{x + \sqrt{a^{2} + x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+(a**2+x**2)**(1/2))**(1/2)/(a**2+x**2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x + \sqrt{a^{2} + x^{2}}}}{\sqrt{a^{2} + x^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + sqrt(a^2 + x^2))/sqrt(a^2 + x^2),x, algorithm="giac")
[Out]