Optimal. Leaf size=18 \[ -\frac{1}{2 b \sqrt{a+b x^4}} \]
[Out]
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Rubi [A] time = 0.0104478, antiderivative size = 18, 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 \[ -\frac{1}{2 b \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.13264, size = 15, normalized size = 0.83 \[ - \frac{1}{2 b \sqrt{a + b x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x**4+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00953613, size = 18, normalized size = 1. \[ -\frac{1}{2 b \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 15, normalized size = 0.8 \[ -{\frac{1}{2\,b}{\frac{1}{\sqrt{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x^4+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.44309, size = 19, normalized size = 1.06 \[ -\frac{1}{2 \, \sqrt{b x^{4} + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^4 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264633, size = 19, normalized size = 1.06 \[ -\frac{1}{2 \, \sqrt{b x^{4} + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^4 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.90867, size = 26, normalized size = 1.44 \[ \begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x**4+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217604, size = 19, normalized size = 1.06 \[ -\frac{1}{2 \, \sqrt{b x^{4} + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^4 + a)^(3/2),x, algorithm="giac")
[Out]