Optimal. Leaf size=18 \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0032332, antiderivative size = 18, normalized size of antiderivative = 1., 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} \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{16-x^4}} \, dx &=-\frac{\sqrt{16-x^4}}{32 x^2}\\ \end{align*}
Mathematica [A] time = 0.0030018, size = 18, normalized size = 1. \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 26, normalized size = 1.4 \begin{align*}{\frac{ \left ( -2+x \right ) \left ( 2+x \right ) \left ({x}^{2}+4 \right ) }{32\,{x}^{2}}{\frac{1}{\sqrt{-{x}^{4}+16}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.98445, size = 19, normalized size = 1.06 \begin{align*} -\frac{\sqrt{-x^{4} + 16}}{32 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.51083, size = 36, normalized size = 2. \begin{align*} -\frac{\sqrt{-x^{4} + 16}}{32 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.768701, size = 32, normalized size = 1.78 \begin{align*} \begin{cases} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{32} & \text{for}\: \frac{16}{\left |{x^{4}}\right |} > 1 \\- \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{32} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.16789, size = 15, normalized size = 0.83 \begin{align*} -\frac{1}{32} \, \sqrt{\frac{16}{x^{4}} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]