Optimal. Leaf size=13 \[ \frac {1}{8} \left (-1+x^6\right )^{4/3} \]
[Out]
________________________________________________________________________________________
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 = {267}
\begin {gather*} \frac {1}{8} \left (x^6-1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 267
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 = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{8} \left (-1+x^6\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.27, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {\left (x^{6}-1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
default | \(\frac {\left (x^{6}-1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
risch | \(\frac {\left (x^{6}-1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
trager | \(\left (\frac {x^{6}}{8}-\frac {1}{8}\right ) \left (x^{6}-1\right )^{\frac {1}{3}}\) | \(16\) |
gosper | \(\frac {\left (-1+x \right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right ) \left (x^{6}-1\right )^{\frac {1}{3}}}{8}\) | \(30\) |
meijerg | \(\frac {\mathrm {signum}\left (x^{6}-1\right )^{\frac {1}{3}} x^{6} \hypergeom \left (\left [-\frac {1}{3}, 1\right ], \left [2\right ], x^{6}\right )}{6 \left (-\mathrm {signum}\left (x^{6}-1\right )\right )^{\frac {1}{3}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, 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]
________________________________________________________________________________________
Fricas [A]
time = 0.38, 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]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 22 vs.
\(2 (8) = 16\).
time = 0.13, 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]
________________________________________________________________________________________
Giac [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]
________________________________________________________________________________________
Mupad [B]
time = 0.14, 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]
________________________________________________________________________________________