Optimal. Leaf size=19 \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
[Out]
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Rubi [A] time = 0.0112074, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
Antiderivative was successfully verified.
[In] Int[x^3/Sqrt[a - b*x^4],x]
[Out]
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Rubi in Sympy [A] time = 2.38299, size = 14, normalized size = 0.74 \[ - \frac{\sqrt{a - b x^{4}}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(-b*x**4+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00816565, size = 19, normalized size = 1. \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/Sqrt[a - b*x^4],x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \[ -{\frac{1}{2\,b}\sqrt{-b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(-b*x^4+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.43872, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(-b*x^4 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225568, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(-b*x^4 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.68569, size = 24, normalized size = 1.26 \[ \begin{cases} - \frac{\sqrt{a - b x^{4}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(-b*x**4+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215174, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(-b*x^4 + a),x, algorithm="giac")
[Out]