Integrand size = 13, antiderivative size = 13 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \left (-1+x^6\right )^{3/2} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267} \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \left (x^6-1\right )^{3/2} \]
[In]
[Out]
Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} \left (-1+x^6\right )^{3/2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \left (-1+x^6\right )^{3/2} \]
[In]
[Out]
Time = 1.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {\left (x^{6}-1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
default | \(\frac {\left (x^{6}-1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
risch | \(\frac {\left (x^{6}-1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
pseudoelliptic | \(\frac {\left (x^{6}-1\right )^{\frac {3}{2}}}{9}\) | \(10\) |
trager | \(\left (\frac {x^{6}}{9}-\frac {1}{9}\right ) \sqrt {x^{6}-1}\) | \(16\) |
gosper | \(\frac {\left (x -1\right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right ) \sqrt {x^{6}-1}}{9}\) | \(30\) |
meijerg | \(\frac {\sqrt {\operatorname {signum}\left (x^{6}-1\right )}\, \left (\frac {4 \sqrt {\pi }}{3}-\frac {2 \sqrt {\pi }\, \left (-2 x^{6}+2\right ) \sqrt {-x^{6}+1}}{3}\right )}{12 \sqrt {\pi }\, \sqrt {-\operatorname {signum}\left (x^{6}-1\right )}}\) | \(51\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (8) = 16\).
Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.69 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {x^{6} \sqrt {x^{6} - 1}}{9} - \frac {\sqrt {x^{6} - 1}}{9} \]
[In]
[Out]
none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \]
[In]
[Out]
Time = 5.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt {-1+x^6} \, dx=\frac {{\left (x^6-1\right )}^{3/2}}{9} \]
[In]
[Out]