Optimal. Leaf size=31 \[ -\frac {x^3}{3}-\frac {2 \tan ^{-1}\left (\frac {1-2 x^3}{\sqrt {3}}\right )}{3 \sqrt {3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {1474, 773, 618, 204} \[ -\frac {x^3}{3}-\frac {2 \tan ^{-1}\left (\frac {1-2 x^3}{\sqrt {3}}\right )}{3 \sqrt {3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 204
Rule 618
Rule 773
Rule 1474
Rubi steps
\begin {align*} \int \frac {x^5 \left (1-x^3\right )}{1-x^3+x^6} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(1-x) x}{1-x+x^2} \, dx,x,x^3\right )\\ &=-\frac {x^3}{3}+\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{1-x+x^2} \, dx,x,x^3\right )\\ &=-\frac {x^3}{3}-\frac {2}{3} \operatorname {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,-1+2 x^3\right )\\ &=-\frac {x^3}{3}-\frac {2 \tan ^{-1}\left (\frac {1-2 x^3}{\sqrt {3}}\right )}{3 \sqrt {3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ \frac {2 \tan ^{-1}\left (\frac {2 x^3-1}{\sqrt {3}}\right )}{3 \sqrt {3}}-\frac {x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 24, normalized size = 0.77 \[ -\frac {1}{3} \, x^{3} + \frac {2}{9} \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x^{3} - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.58, size = 24, normalized size = 0.77 \[ -\frac {1}{3} \, x^{3} + \frac {2}{9} \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x^{3} - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 25, normalized size = 0.81 \[ -\frac {x^{3}}{3}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\left (2 x^{3}-1\right ) \sqrt {3}}{3}\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.96, size = 24, normalized size = 0.77 \[ -\frac {1}{3} \, x^{3} + \frac {2}{9} \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x^{3} - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 26, normalized size = 0.84 \[ -\frac {2\,\sqrt {3}\,\mathrm {atan}\left (\frac {\sqrt {3}}{3}-\frac {2\,\sqrt {3}\,x^3}{3}\right )}{9}-\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 32, normalized size = 1.03 \[ - \frac {x^{3}}{3} + \frac {2 \sqrt {3} \operatorname {atan}{\left (\frac {2 \sqrt {3} x^{3}}{3} - \frac {\sqrt {3}}{3} \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________