Optimal. Leaf size=40 \[ \frac{1}{15} \left (x^6+2\right )^{5/2}-\frac{4}{9} \left (x^6+2\right )^{3/2}+\frac{4 \sqrt{x^6+2}}{3} \]
[Out]
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Rubi [A] time = 0.0389995, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{15} \left (x^6+2\right )^{5/2}-\frac{4}{9} \left (x^6+2\right )^{3/2}+\frac{4 \sqrt{x^6+2}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^17/Sqrt[2 + x^6],x]
[Out]
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Rubi in Sympy [A] time = 4.47041, size = 32, normalized size = 0.8 \[ \frac{\left (x^{6} + 2\right )^{\frac{5}{2}}}{15} - \frac{4 \left (x^{6} + 2\right )^{\frac{3}{2}}}{9} + \frac{4 \sqrt{x^{6} + 2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**17/(x**6+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0132902, size = 25, normalized size = 0.62 \[ \frac{1}{45} \sqrt{x^6+2} \left (3 x^{12}-8 x^6+32\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^17/Sqrt[2 + x^6],x]
[Out]
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Maple [A] time = 0.006, size = 22, normalized size = 0.6 \[{\frac{3\,{x}^{12}-8\,{x}^{6}+32}{45}\sqrt{{x}^{6}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^17/(x^6+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.41831, size = 38, normalized size = 0.95 \[ \frac{1}{15} \,{\left (x^{6} + 2\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{6} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/sqrt(x^6 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22035, size = 28, normalized size = 0.7 \[ \frac{1}{45} \,{\left (3 \, x^{12} - 8 \, x^{6} + 32\right )} \sqrt{x^{6} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/sqrt(x^6 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 15.8572, size = 39, normalized size = 0.98 \[ \frac{x^{12} \sqrt{x^{6} + 2}}{15} - \frac{8 x^{6} \sqrt{x^{6} + 2}}{45} + \frac{32 \sqrt{x^{6} + 2}}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**17/(x**6+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220276, size = 38, normalized size = 0.95 \[ \frac{1}{15} \,{\left (x^{6} + 2\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{6} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/sqrt(x^6 + 2),x, algorithm="giac")
[Out]