Optimal. Leaf size=14 \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{2} \left (x^3-3\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {1352, 618, 204} \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{2} \left (x^3-3\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 204
Rule 618
Rule 1352
Rubi steps
\begin {align*} \int \frac {x^2}{13-6 x^3+x^6} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{13-6 x+x^2} \, dx,x,x^3\right )\\ &=-\left (\frac {2}{3} \operatorname {Subst}\left (\int \frac {1}{-16-x^2} \, dx,x,2 \left (-3+x^3\right )\right )\right )\\ &=\frac {1}{6} \tan ^{-1}\left (\frac {1}{2} \left (-3+x^3\right )\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{2} \left (x^3-3\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 16, normalized size = 1.14 \[ -\frac {1}{6} \tan ^{-1}\left (\frac {3}{2}-\frac {x^3}{2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.24, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{2} \, x^{3} - \frac {3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.99, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{2} \, x^{3} - \frac {3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 11, normalized size = 0.79
method | result | size |
default | \(\frac {\arctan \left (\frac {x^{3}}{2}-\frac {3}{2}\right )}{6}\) | \(11\) |
risch | \(\frac {\arctan \left (\frac {x^{3}}{2}-\frac {3}{2}\right )}{6}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.96, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{2} \, x^{3} - \frac {3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 10, normalized size = 0.71 \[ \frac {\mathrm {atan}\left (\frac {x^3}{2}-\frac {3}{2}\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 10, normalized size = 0.71 \[ \frac {\operatorname {atan}{\left (\frac {x^{3}}{2} - \frac {3}{2} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________