Optimal. Leaf size=23 \[ \frac {2}{9} (x+1)^{3/2} \left (x^2-x+1\right )^{3/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {913} \[ \frac {2}{9} (x+1)^{3/2} \left (x^2-x+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 913
Rubi steps
\begin {align*} \int x^2 \sqrt {1+x} \sqrt {1-x+x^2} \, dx &=\frac {2}{9} (1+x)^{3/2} \left (1-x+x^2\right )^{3/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 23, normalized size = 1.00 \[ \frac {2}{9} (x+1)^{3/2} \left (x^2-x+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.02, size = 22, normalized size = 0.96 \[ \frac {2}{9} \, {\left (x^{3} + 1\right )} \sqrt {x^{2} - x + 1} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.24, size = 67, normalized size = 2.91 \[ \frac {2}{315} \, {\left ({\left (5 \, {\left (7 \, x - 23\right )} {\left (x + 1\right )} + 258\right )} {\left (x + 1\right )} - 213\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} + \frac {2}{105} \, {\left (3 \, {\left (5 \, x - 12\right )} {\left (x + 1\right )} + 71\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ \frac {2 \left (x +1\right )^{\frac {3}{2}} \left (x^{2}-x +1\right )^{\frac {3}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.95, size = 22, normalized size = 0.96 \[ \frac {2}{9} \, {\left (x^{3} + 1\right )} \sqrt {x^{2} - x + 1} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.62, size = 22, normalized size = 0.96 \[ \frac {2\,\left (x^3+1\right )\,\sqrt {x+1}\,\sqrt {x^2-x+1}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{2} \sqrt {x + 1} \sqrt {x^{2} - x + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________