Optimal. Leaf size=21 \[ -\frac {4 \left (-x^5+x^4-1\right )^{5/4}}{5 x^5} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1590} \begin {gather*} -\frac {4 \left (-x^5+x^4-1\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1590
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{-1+x^4-x^5} \left (-4+x^5\right )}{x^6} \, dx &=-\frac {4 \left (-1+x^4-x^5\right )^{5/4}}{5 x^5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 21, normalized size = 1.00 \begin {gather*} -\frac {4 \left (-x^5+x^4-1\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.26, size = 21, normalized size = 1.00 \begin {gather*} -\frac {4 \left (-1+x^4-x^5\right )^{5/4}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 27, normalized size = 1.29 \begin {gather*} \frac {4 \, {\left (x^{5} - x^{4} + 1\right )} {\left (-x^{5} + x^{4} - 1\right )}^{\frac {1}{4}}}{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^{5} - 4\right )} {\left (-x^{5} + x^{4} - 1\right )}^{\frac {1}{4}}}{x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 18, normalized size = 0.86
method | result | size |
gosper | \(-\frac {4 \left (-x^{5}+x^{4}-1\right )^{\frac {5}{4}}}{5 x^{5}}\) | \(18\) |
trager | \(\frac {4 \left (x^{5}-x^{4}+1\right ) \left (-x^{5}+x^{4}-1\right )^{\frac {1}{4}}}{5 x^{5}}\) | \(28\) |
risch | \(-\frac {4 \left (x^{10}-2 x^{9}+x^{8}+2 x^{5}-2 x^{4}+1\right )}{5 \left (-x^{5}+x^{4}-1\right )^{\frac {3}{4}} x^{5}}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.74, size = 27, normalized size = 1.29 \begin {gather*} \frac {4 \, {\left (x^{5} - x^{4} + 1\right )} {\left (-x^{5} + x^{4} - 1\right )}^{\frac {1}{4}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.32, size = 17, normalized size = 0.81 \begin {gather*} -\frac {4\,{\left (-x^5+x^4-1\right )}^{5/4}}{5\,x^5} \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 {\left (x^{5} - 4\right ) \sqrt [4]{- x^{5} + x^{4} - 1}}{x^{6}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________