Optimal. Leaf size=16 \[ -\frac {\left (x^3+1\right )^{5/3}}{5 x^5} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, 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 = {264} \begin {gather*} -\frac {\left (x^3+1\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin {align*} \int \frac {\left (1+x^3\right )^{2/3}}{x^6} \, dx &=-\frac {\left (1+x^3\right )^{5/3}}{5 x^5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (x^3+1\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.07, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (1+x^3\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{3} + 1\right )}^{\frac {5}{3}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} + 1\right )}^{\frac {2}{3}}}{x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 13, normalized size = 0.81
method | result | size |
trager | \(-\frac {\left (x^{3}+1\right )^{\frac {5}{3}}}{5 x^{5}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{3}+1\right )^{\frac {5}{3}}}{5 x^{5}}\) | \(13\) |
risch | \(-\frac {x^{6}+2 x^{3}+1}{5 x^{5} \left (x^{3}+1\right )^{\frac {1}{3}}}\) | \(23\) |
gosper | \(-\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (x^{3}+1\right )^{\frac {2}{3}}}{5 x^{5}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{3} + 1\right )}^{\frac {5}{3}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.19, size = 24, normalized size = 1.50 \begin {gather*} -\frac {{\left (x^3+1\right )}^{2/3}+x^3\,{\left (x^3+1\right )}^{2/3}}{5\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.67, size = 53, normalized size = 3.31 \begin {gather*} \frac {\left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {5}{3}\right )}{3 \Gamma \left (- \frac {2}{3}\right )} + \frac {\left (1 + \frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (- \frac {5}{3}\right )}{3 x^{3} \Gamma \left (- \frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________