Optimal. Leaf size=29 \[ \frac {x^2}{6}-\frac {\tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{3 \sqrt {6}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {275, 321, 203} \[ \frac {x^2}{6}-\frac {\tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{3 \sqrt {6}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 203
Rule 275
Rule 321
Rubi steps
\begin {align*} \int \frac {x^5}{2+3 x^4} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {x^2}{2+3 x^2} \, dx,x,x^2\right )\\ &=\frac {x^2}{6}-\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{2+3 x^2} \, dx,x,x^2\right )\\ &=\frac {x^2}{6}-\frac {\tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{3 \sqrt {6}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \[ \frac {x^2}{6}-\frac {\tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{3 \sqrt {6}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 20, normalized size = 0.69 \[ \frac {1}{6} \, x^{2} - \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 20, normalized size = 0.69 \[ \frac {1}{6} \, x^{2} - \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 21, normalized size = 0.72 \[ \frac {x^{2}}{6}-\frac {\sqrt {6}\, \arctan \left (\frac {\sqrt {6}\, x^{2}}{2}\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 2.93, size = 20, normalized size = 0.69 \[ \frac {1}{6} \, x^{2} - \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.01, size = 20, normalized size = 0.69 \[ \frac {x^2}{6}-\frac {\sqrt {6}\,\mathrm {atan}\left (\frac {\sqrt {6}\,x^2}{2}\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 22, normalized size = 0.76 \[ \frac {x^{2}}{6} - \frac {\sqrt {6} \operatorname {atan}{\left (\frac {\sqrt {6} x^{2}}{2} \right )}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________