Optimal. Leaf size=33 \[ \frac{\sqrt{x^8+1}}{6 x^4}-\frac{\sqrt{x^8+1}}{12 x^{12}} \]
[Out]
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Rubi [A] time = 0.026796, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\sqrt{x^8+1}}{6 x^4}-\frac{\sqrt{x^8+1}}{12 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^13*Sqrt[1 + x^8]),x]
[Out]
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Rubi in Sympy [A] time = 3.26514, size = 26, normalized size = 0.79 \[ \frac{\sqrt{x^{8} + 1}}{6 x^{4}} - \frac{\sqrt{x^{8} + 1}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**13/(x**8+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0130553, size = 25, normalized size = 0.76 \[ \left (\frac{1}{6 x^4}-\frac{1}{12 x^{12}}\right ) \sqrt{x^8+1} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^13*Sqrt[1 + x^8]),x]
[Out]
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Maple [A] time = 0.005, size = 20, normalized size = 0.6 \[{\frac{2\,{x}^{8}-1}{12\,{x}^{12}}\sqrt{{x}^{8}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^13/(x^8+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.42842, size = 34, normalized size = 1.03 \[ \frac{\sqrt{x^{8} + 1}}{4 \, x^{4}} - \frac{{\left (x^{8} + 1\right )}^{\frac{3}{2}}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^8 + 1)*x^13),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22847, size = 70, normalized size = 2.12 \[ \frac{3 \, x^{8} - 3 \, \sqrt{x^{8} + 1} x^{4} + 1}{12 \,{\left (4 \, x^{24} + 3 \, x^{16} -{\left (4 \, x^{20} + x^{12}\right )} \sqrt{x^{8} + 1}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^8 + 1)*x^13),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.4109, size = 26, normalized size = 0.79 \[ \frac{\sqrt{1 + \frac{1}{x^{8}}}}{6} - \frac{\sqrt{1 + \frac{1}{x^{8}}}}{12 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**13/(x**8+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.233863, size = 26, normalized size = 0.79 \[ -\frac{1}{12} \,{\left (\frac{1}{x^{8}} + 1\right )}^{\frac{3}{2}} + \frac{1}{4} \, \sqrt{\frac{1}{x^{8}} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^8 + 1)*x^13),x, algorithm="giac")
[Out]