Optimal. Leaf size=18 \[ \frac{\sqrt{-4 x^2-9}}{9 x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0030486, 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} \[ \frac{\sqrt{-4 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{-9-4 x^2}} \, dx &=\frac{\sqrt{-9-4 x^2}}{9 x}\\ \end{align*}
Mathematica [A] time = 0.0021481, size = 18, normalized size = 1. \[ \frac{\sqrt{-4 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 15, normalized size = 0.8 \begin{align*}{\frac{1}{9\,x}\sqrt{-4\,{x}^{2}-9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 3.66322, size = 19, normalized size = 1.06 \begin{align*} \frac{\sqrt{-4 \, x^{2} - 9}}{9 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.18863, size = 32, normalized size = 1.78 \begin{align*} \frac{\sqrt{-4 \, x^{2} - 9}}{9 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [C] time = 0.7266, size = 15, normalized size = 0.83 \begin{align*} \frac{2 i \sqrt{1 + \frac{9}{4 x^{2}}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [C] time = 2.56933, size = 50, normalized size = 2.78 \begin{align*} \frac{i \, \sqrt{4 \, x^{2} + 9} + 3 i}{18 \, x} + \frac{8 \, x}{9 \,{\left (-4 i \, \sqrt{4 \, x^{2} + 9} - 12 i\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]