Optimal. Leaf size=45 \[ -\sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right )-\frac{x^9}{3 \sqrt{x^6+2}}+\frac{1}{2} \sqrt{x^6+2} x^3 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.055127, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ -\sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right )-\frac{x^9}{3 \sqrt{x^6+2}}+\frac{1}{2} \sqrt{x^6+2} x^3 \]
Antiderivative was successfully verified.
[In] Int[x^14/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.49788, size = 37, normalized size = 0.82 \[ - \frac{x^{9}}{3 \sqrt{x^{6} + 2}} + \frac{x^{3} \sqrt{x^{6} + 2}}{2} - \operatorname{asinh}{\left (\frac{\sqrt{2} x^{3}}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**14/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0386232, size = 43, normalized size = 0.96 \[ \frac{x^9+6 x^3-6 \sqrt{x^6+2} \sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right )}{6 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^14/(2 + x^6)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.034, size = 30, normalized size = 0.7 \[{\frac{{x}^{3} \left ({x}^{6}+6 \right ) }{6}{\frac{1}{\sqrt{{x}^{6}+2}}}}-{\it Arcsinh} \left ({\frac{{x}^{3}\sqrt{2}}{2}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^14/(x^6+2)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.436, size = 99, normalized size = 2.2 \[ -\frac{\frac{3 \,{\left (x^{6} + 2\right )}}{x^{6}} - 2}{3 \,{\left (\frac{\sqrt{x^{6} + 2}}{x^{3}} - \frac{{\left (x^{6} + 2\right )}^{\frac{3}{2}}}{x^{9}}\right )}} - \frac{1}{2} \, \log \left (\frac{\sqrt{x^{6} + 2}}{x^{3}} + 1\right ) + \frac{1}{2} \, \log \left (\frac{\sqrt{x^{6} + 2}}{x^{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(x^6 + 2)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.220444, size = 170, normalized size = 3.78 \[ -\frac{2 \, x^{18} + 7 \, x^{12} - 2 \, x^{6} - 6 \,{\left (2 \, x^{12} + 5 \, x^{6} -{\left (2 \, x^{9} + 3 \, x^{3}\right )} \sqrt{x^{6} + 2} + 2\right )} \log \left (-x^{3} + \sqrt{x^{6} + 2}\right ) -{\left (2 \, x^{15} + 5 \, x^{9} - 6 \, x^{3}\right )} \sqrt{x^{6} + 2} - 8}{6 \,{\left (2 \, x^{12} + 5 \, x^{6} -{\left (2 \, x^{9} + 3 \, x^{3}\right )} \sqrt{x^{6} + 2} + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(x^6 + 2)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 14.939, size = 36, normalized size = 0.8 \[ \frac{x^{9}}{6 \sqrt{x^{6} + 2}} + \frac{x^{3}}{\sqrt{x^{6} + 2}} - \operatorname{asinh}{\left (\frac{\sqrt{2} x^{3}}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**14/(x**6+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{14}}{{\left (x^{6} + 2\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(x^6 + 2)^(3/2),x, algorithm="giac")
[Out]