Optimal. Leaf size=18 \[ -\frac {\sqrt {1-x^4}}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ -\frac {\sqrt {1-x^4}}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt {1-x^4}} \, dx &=-\frac {\sqrt {1-x^4}}{2 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ -\frac {\sqrt {1-x^4}}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.71, size = 14, normalized size = 0.78 \[ -\frac {\sqrt {-x^{4} + 1}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.17, size = 35, normalized size = 1.94 \[ \frac {x^{2}}{4 \, {\left (\sqrt {-x^{4} + 1} - 1\right )}} - \frac {\sqrt {-x^{4} + 1} - 1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 26, normalized size = 1.44 \[ \frac {\left (x -1\right ) \left (x +1\right ) \left (x^{2}+1\right )}{2 \sqrt {-x^{4}+1}\, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 14, normalized size = 0.78 \[ -\frac {\sqrt {-x^{4} + 1}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.12, size = 14, normalized size = 0.78 \[ -\frac {\sqrt {1-x^4}}{2\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.18, size = 34, normalized size = 1.89 \[ \begin {cases} - \frac {i \sqrt {x^{4} - 1}}{2 x^{2}} & \text {for}\: \left |{x^{4}}\right | > 1 \\- \frac {\sqrt {1 - x^{4}}}{2 x^{2}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________