Optimal. Leaf size=16 \[ \frac{x}{a \sqrt{a+b x^2}} \]
[Out]
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Rubi [A] time = 0.00889905, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x}{a \sqrt{a+b x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.27352, size = 12, normalized size = 0.75 \[ \frac{x}{a \sqrt{a + b x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**2+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.01152, size = 16, normalized size = 1. \[ \frac{x}{a \sqrt{a+b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^(-3/2),x]
[Out]
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Maple [A] time = 0., size = 15, normalized size = 0.9 \[{\frac{x}{a}{\frac{1}{\sqrt{b{x}^{2}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x^2+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.35486, size = 19, normalized size = 1.19 \[ \frac{x}{\sqrt{b x^{2} + a} a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(-3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206676, size = 31, normalized size = 1.94 \[ \frac{\sqrt{b x^{2} + a} x}{a b x^{2} + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(-3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.80627, size = 17, normalized size = 1.06 \[ \frac{x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x**2+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224857, size = 19, normalized size = 1.19 \[ \frac{x}{\sqrt{b x^{2} + a} a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(-3/2),x, algorithm="giac")
[Out]