Optimal. Leaf size=13 \[ \frac {1}{8} \left (x^6+1\right )^{4/3} \]
________________________________________________________________________________________
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 = {261} \begin {gather*} \frac {1}{8} \left (x^6+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin {align*} \int x^5 \sqrt [3]{1+x^6} \, dx &=\frac {1}{8} \left (1+x^6\right )^{4/3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{8} \left (x^6+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{8} \left (x^6+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8} \, {\left (x^{6} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8} \, {\left (x^{6} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 25, normalized size = 1.92 \begin {gather*} \frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right ) \left (x^{6}+1\right )^{\frac {1}{3}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8} \, {\left (x^{6} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (x^6+1\right )}^{4/3}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.34, size = 22, normalized size = 1.69 \begin {gather*} \frac {x^{6} \sqrt [3]{x^{6} + 1}}{8} + \frac {\sqrt [3]{x^{6} + 1}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________