Optimal. Leaf size=13 \[ \frac {\sqrt {2+x^6}}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267}
\begin {gather*} \frac {\sqrt {x^6+2}}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 267
Rubi steps
\begin {align*} \int \frac {x^5}{\sqrt {2+x^6}} \, dx &=\frac {\sqrt {2+x^6}}{3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {\sqrt {2+x^6}}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.16, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {\sqrt {x^{6}+2}}{3}\) | \(10\) |
derivativedivides | \(\frac {\sqrt {x^{6}+2}}{3}\) | \(10\) |
default | \(\frac {\sqrt {x^{6}+2}}{3}\) | \(10\) |
trager | \(\frac {\sqrt {x^{6}+2}}{3}\) | \(10\) |
risch | \(\frac {\sqrt {x^{6}+2}}{3}\) | \(10\) |
meijerg | \(\frac {\sqrt {2}\, \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1+\frac {x^{6}}{2}}\right )}{6 \sqrt {\pi }}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, \sqrt {x^{6} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, \sqrt {x^{6} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 8, normalized size = 0.62 \begin {gather*} \frac {\sqrt {x^{6} + 2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.27, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, \sqrt {x^{6} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.15, size = 9, normalized size = 0.69 \begin {gather*} \frac {\sqrt {x^6+2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________