Optimal. Leaf size=13 \[ \frac {1}{8 \left (1-x^2\right )^4} \]
[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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {267}
\begin {gather*} \frac {1}{8 \left (1-x^2\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 267
Rubi steps
\begin {align*} \int \frac {x}{\left (1-x^2\right )^5} \, dx &=\frac {1}{8 \left (1-x^2\right )^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{8 \left (-1+x^2\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.19, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {1}{8 \left (x^{2}-1\right )^{4}}\) | \(10\) |
default | \(\frac {1}{8 \left (x^{2}-1\right )^{4}}\) | \(10\) |
norman | \(\frac {1}{8 \left (x^{2}-1\right )^{4}}\) | \(10\) |
risch | \(\frac {1}{8 \left (x^{2}-1\right )^{4}}\) | \(10\) |
derivativedivides | \(\frac {1}{8 \left (-x^{2}+1\right )^{4}}\) | \(12\) |
meijerg | \(\frac {x^{2} \left (-x^{6}+4 x^{4}-6 x^{2}+4\right )}{8 \left (-x^{2}+1\right )^{4}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8 \, {\left (x^{2} - 1\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 24 vs.
\(2 (9) = 18\).
time = 0.38, size = 24, normalized size = 1.85 \begin {gather*} \frac {1}{8 \, {\left (x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right )}} \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 = 0.04, size = 22, normalized size = 1.69 \begin {gather*} \frac {1}{8 x^{8} - 32 x^{6} + 48 x^{4} - 32 x^{2} + 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.75, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8 \, {\left (x^{2} - 1\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8\,{\left (x^2-1\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________