Optimal. Leaf size=15 \[ \frac{1}{2 \sqrt{1-x^4}} \]
[Out]
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Rubi [A] time = 0.00808117, antiderivative size = 15, 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 \[ \frac{1}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Int[x^3/(1 - x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.92273, size = 10, normalized size = 0.67 \[ \frac{1}{2 \sqrt{- x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(-x**4+1)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00484006, size = 15, normalized size = 1. \[ \frac{1}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(1 - x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 23, normalized size = 1.5 \[ -{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) }{2} \left ( -{x}^{4}+1 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(-x^4+1)^(3/2),x)
[Out]
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Maxima [A] time = 1.43415, size = 15, normalized size = 1. \[ \frac{1}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.279419, size = 15, normalized size = 1. \[ \frac{1}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.36861, size = 10, normalized size = 0.67 \[ \frac{1}{2 \sqrt{- x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(-x**4+1)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213182, size = 15, normalized size = 1. \[ \frac{1}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]