Optimal. Leaf size=8 \[ \frac{\tan ^{-1}(x)}{\sqrt{2}} \]
[Out]
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Rubi [A] time = 0.00793174, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{\tan ^{-1}(x)}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 + x^2]*Sqrt[2 + 2*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 2.52358, size = 8, normalized size = 1. \[ \frac{\sqrt{2} \operatorname{atan}{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2+1)**(1/2)/(2*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00708218, size = 8, normalized size = 1. \[ \frac{\tan ^{-1}(x)}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 + x^2]*Sqrt[2 + 2*x^2]),x]
[Out]
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Maple [A] time = 0.031, size = 8, normalized size = 1. \[{\frac{\arctan \left ( x \right ) \sqrt{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2+1)^(1/2)/(2*x^2+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.52895, size = 9, normalized size = 1.12 \[ \frac{1}{2} \, \sqrt{2} \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*x^2 + 2)*sqrt(x^2 + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244895, size = 46, normalized size = 5.75 \[ -\frac{1}{4} \, \sqrt{2} \arctan \left (\frac{\sqrt{2} \sqrt{2 \, x^{2} + 2} \sqrt{x^{2} + 1} x}{x^{4} - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*x^2 + 2)*sqrt(x^2 + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.5482, size = 8, normalized size = 1. \[ \frac{\sqrt{2} \operatorname{atan}{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2+1)**(1/2)/(2*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.225048, size = 9, normalized size = 1.12 \[ \frac{1}{2} \, \sqrt{2} \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(2*x^2 + 2)*sqrt(x^2 + 1)),x, algorithm="giac")
[Out]