Optimal. Leaf size=27 \[ \frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0108826, antiderivative size = 27, 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, Rules used = {266, 43} \[ \frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{11}}{\left (2+x^6\right )^{3/2}} \, dx &=\frac{1}{6} \operatorname{Subst}\left (\int \frac{x}{(2+x)^{3/2}} \, dx,x,x^6\right )\\ &=\frac{1}{6} \operatorname{Subst}\left (\int \left (-\frac{2}{(2+x)^{3/2}}+\frac{1}{\sqrt{2+x}}\right ) \, dx,x,x^6\right )\\ &=\frac{2}{3 \sqrt{2+x^6}}+\frac{\sqrt{2+x^6}}{3}\\ \end{align*}
Mathematica [A] time = 0.0053689, size = 18, normalized size = 0.67 \[ \frac{x^6+4}{3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 15, normalized size = 0.6 \begin{align*}{\frac{{x}^{6}+4}{3}{\frac{1}{\sqrt{{x}^{6}+2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.983694, size = 26, normalized size = 0.96 \begin{align*} \frac{1}{3} \, \sqrt{x^{6} + 2} + \frac{2}{3 \, \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.41825, size = 39, normalized size = 1.44 \begin{align*} \frac{x^{6} + 4}{3 \, \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.37388, size = 24, normalized size = 0.89 \begin{align*} \frac{x^{6}}{3 \sqrt{x^{6} + 2}} + \frac{4}{3 \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14739, size = 26, normalized size = 0.96 \begin{align*} \frac{1}{3} \, \sqrt{x^{6} + 2} + \frac{2}{3 \, \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]