Optimal. Leaf size=34 \[ \frac{1}{2} x \left (x^{2 n}\right )^{\left .-\frac{1}{2}\right /n} \tan ^{-1}\left (2 \left (x^{2 n}\right )^{\left .\frac{1}{2}\right /n}\right ) \]
[Out]
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Rubi [A] time = 0.0159857, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{2} x \left (x^{2 n}\right )^{\left .-\frac{1}{2}\right /n} \tan ^{-1}\left (2 \left (x^{2 n}\right )^{\left .\frac{1}{2}\right /n}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + 4*(x^(2*n))^n^(-1))^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.56992, size = 26, normalized size = 0.76 \[ \frac{x \left (x^{2 n}\right )^{- \frac{1}{2 n}} \operatorname{atan}{\left (2 \left (x^{2 n}\right )^{\frac{1}{2 n}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+4*(x**(2*n))**(1/n)),x)
[Out]
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Mathematica [A] time = 2.17893, size = 0, normalized size = 0. \[ \int \frac{1}{1+4 \left (x^{2 n}\right )^{\frac{1}{n}}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(1 + 4*(x^(2*n))^n^(-1))^(-1),x]
[Out]
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Maple [A] time = 0.107, size = 29, normalized size = 0.9 \[{\frac{x}{2} \left ({x}^{2\,n} \right ) ^{-{\frac{1}{2\,n}}}\arctan \left ( 2\, \left ({x}^{2\,n} \right ) ^{1/2\,{n}^{-1}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+4*(x^(2*n))^(1/n)),x)
[Out]
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Maxima [A] time = 22.419, size = 8, normalized size = 0.24 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*(x^(2*n))^(1/n) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249771, size = 8, normalized size = 0.24 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*(x^(2*n))^(1/n) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.174254, size = 5, normalized size = 0.15 \[ \frac{\operatorname{atan}{\left (2 x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+4*(x**(2*n))**(1/n)),x)
[Out]
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GIAC/XCAS [A] time = 0.216322, size = 8, normalized size = 0.24 \[ \frac{1}{2} \, \arctan \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*(x^(2*n))^(1/n) + 1),x, algorithm="giac")
[Out]