Optimal. Leaf size=21 \[ -\frac{\left (a+b x^2\right )^{3/2}}{3 a x^3} \]
[Out]
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Rubi [A] time = 0.0219531, antiderivative size = 21, 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 \[ -\frac{\left (a+b x^2\right )^{3/2}}{3 a x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*x^2]/x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.1768, size = 17, normalized size = 0.81 \[ - \frac{\left (a + b x^{2}\right )^{\frac{3}{2}}}{3 a x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**(1/2)/x**4,x)
[Out]
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Mathematica [A] time = 0.0151685, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^2\right )^{3/2}}{3 a x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b*x^2]/x^4,x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.9 \[ -{\frac{1}{3\,a{x}^{3}} \left ( b{x}^{2}+a \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^(1/2)/x^4,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2 + a)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234115, size = 23, normalized size = 1.1 \[ -\frac{{\left (b x^{2} + a\right )}^{\frac{3}{2}}}{3 \, a x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2 + a)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.0858, size = 42, normalized size = 2. \[ - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**(1/2)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.211832, size = 80, normalized size = 3.81 \[ \frac{2 \,{\left (3 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{4} b^{\frac{3}{2}} + a^{2} b^{\frac{3}{2}}\right )}}{3 \,{\left ({\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} - a\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2 + a)/x^4,x, algorithm="giac")
[Out]