Optimal. Leaf size=20 \[ \frac {3 \left (x^6-x^2\right )^{2/3}}{8 x^4} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2014} \begin {gather*} \frac {3 \left (x^6-x^2\right )^{2/3}}{8 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2014
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt [3]{-x^2+x^6}} \, dx &=\frac {3 \left (-x^2+x^6\right )^{2/3}}{8 x^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {3 \left (x^2 \left (x^4-1\right )\right )^{2/3}}{8 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.32, size = 20, normalized size = 1.00 \begin {gather*} \frac {3 \left (-x^2+x^6\right )^{2/3}}{8 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 16, normalized size = 0.80 \begin {gather*} \frac {3 \, {\left (x^{6} - x^{2}\right )}^{\frac {2}{3}}}{8 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.43, size = 11, normalized size = 0.55 \begin {gather*} \frac {3}{8} \, {\left (-\frac {1}{x^{4}} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 17, normalized size = 0.85
method | result | size |
trager | \(\frac {3 \left (x^{6}-x^{2}\right )^{\frac {2}{3}}}{8 x^{4}}\) | \(17\) |
risch | \(\frac {\frac {3 x^{4}}{8}-\frac {3}{8}}{x^{2} \left (x^{2} \left (x^{4}-1\right )\right )^{\frac {1}{3}}}\) | \(22\) |
gosper | \(\frac {3 \left (-1+x \right ) \left (1+x \right ) \left (x^{2}+1\right )}{8 x^{2} \left (x^{6}-x^{2}\right )^{\frac {1}{3}}}\) | \(28\) |
meijerg | \(-\frac {3 \left (-\mathrm {signum}\left (x^{4}-1\right )\right )^{\frac {1}{3}} \left (-x^{4}+1\right )^{\frac {2}{3}}}{8 \mathrm {signum}\left (x^{4}-1\right )^{\frac {1}{3}} x^{\frac {8}{3}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 30, normalized size = 1.50 \begin {gather*} \frac {3 \, {\left (x^{6} - x^{2}\right )}}{8 \, {\left (x^{2} + 1\right )}^{\frac {1}{3}} {\left (x^{2} - 1\right )}^{\frac {1}{3}} {\left (x^{2}\right )}^{\frac {7}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.24, size = 16, normalized size = 0.80 \begin {gather*} \frac {3\,{\left (x^6-x^2\right )}^{2/3}}{8\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{3} \sqrt [3]{x^{2} \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________