Optimal. Leaf size=18 \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0126077, 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 \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(7/2)*Sqrt[1 + x^5]),x]
[Out]
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Rubi in Sympy [A] time = 2.21964, size = 17, normalized size = 0.94 \[ - \frac{2 \sqrt{x^{5} + 1}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(7/2)/(x**5+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0106426, size = 18, normalized size = 1. \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(7/2)*Sqrt[1 + x^5]),x]
[Out]
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Maple [B] time = 0.006, size = 32, normalized size = 1.8 \[ -{\frac{ \left ( 2+2\,x \right ) \left ({x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) }{5}{x}^{-{\frac{5}{2}}}{\frac{1}{\sqrt{{x}^{5}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(7/2)/(x^5+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.43771, size = 16, normalized size = 0.89 \[ -\frac{2 \, \sqrt{x^{5} + 1}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^5 + 1)*x^(7/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227658, size = 16, normalized size = 0.89 \[ -\frac{2 \, \sqrt{x^{5} + 1}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^5 + 1)*x^(7/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 133.216, size = 14, normalized size = 0.78 \[ - \frac{2 \sqrt{1 + \frac{1}{x^{5}}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(7/2)/(x**5+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.225452, size = 15, normalized size = 0.83 \[ -\frac{2}{5} \, \sqrt{\frac{1}{x^{5}} + 1} + \frac{2}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^5 + 1)*x^(7/2)),x, algorithm="giac")
[Out]