Optimal. Leaf size=14 \[ \frac{g x}{\sqrt{a+b x^4}} \]
[Out]
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Rubi [A] time = 0.0117671, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ \frac{g x}{\sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Int[(a*g - b*g*x^4)/(a + b*x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 6.02304, size = 12, normalized size = 0.86 \[ \frac{g x}{\sqrt{a + b x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*g*x**4+a*g)/(b*x**4+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0249728, size = 14, normalized size = 1. \[ \frac{g x}{\sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[(a*g - b*g*x^4)/(a + b*x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 13, normalized size = 0.9 \[{gx{\frac{1}{\sqrt{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*g*x^4+a*g)/(b*x^4+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.55461, size = 16, normalized size = 1.14 \[ \frac{g x}{\sqrt{b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*g*x^4 - a*g)/(b*x^4 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216265, size = 16, normalized size = 1.14 \[ \frac{g x}{\sqrt{b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*g*x^4 - a*g)/(b*x^4 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.5294, size = 80, normalized size = 5.71 \[ \frac{g x \Gamma \left (\frac{1}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 \sqrt{a} \Gamma \left (\frac{5}{4}\right )} - \frac{b g x^{5} \Gamma \left (\frac{5}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 a^{\frac{3}{2}} \Gamma \left (\frac{9}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*g*x**4+a*g)/(b*x**4+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214519, size = 16, normalized size = 1.14 \[ \frac{g x}{\sqrt{b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*g*x^4 - a*g)/(b*x^4 + a)^(3/2),x, algorithm="giac")
[Out]