Optimal. Leaf size=23 \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
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Rubi [A] time = 0.0202456, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(7/2)*Sqrt[a + b*x^5]),x]
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Rubi in Sympy [A] time = 2.76954, size = 20, normalized size = 0.87 \[ - \frac{2 \sqrt{a + b x^{5}}}{5 a x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(7/2)/(b*x**5+a)**(1/2),x)
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Mathematica [A] time = 0.0192553, size = 23, normalized size = 1. \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(7/2)*Sqrt[a + b*x^5]),x]
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Maple [A] time = 0.006, size = 18, normalized size = 0.8 \[ -{\frac{2}{5\,a}\sqrt{b{x}^{5}+a}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(7/2)/(b*x^5+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.44606, size = 23, normalized size = 1. \[ -\frac{2 \, \sqrt{b x^{5} + a}}{5 \, a x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(7/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223865, size = 23, normalized size = 1. \[ -\frac{2 \, \sqrt{b x^{5} + a}}{5 \, a x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(7/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 152.634, size = 22, normalized size = 0.96 \[ - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x^{5}} + 1}}{5 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(7/2)/(b*x**5+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.232367, size = 31, normalized size = 1.35 \[ -\frac{2 \, \sqrt{b + \frac{a}{x^{5}}}}{5 \, a} + \frac{2 \, \sqrt{b}}{5 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(7/2)),x, algorithm="giac")
[Out]