Optimal. Leaf size=27 \[ \frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0227884, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038, Rules used = {8} \[ \frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx &=\frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}}\\ \end{align*}
Mathematica [A] time = 0.0000354, size = 27, normalized size = 1. \[ \frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 26, normalized size = 1. \begin{align*}{\frac{x}{r}{\frac{1}{\sqrt{-2\,K{r}^{4}+2\,H{r}^{2}-{a}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.927586, size = 34, normalized size = 1.26 \begin{align*} \frac{x}{\sqrt{-2 \, K r^{4} + 2 \, H r^{2} - a^{2}} r} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.8654, size = 85, normalized size = 3.15 \begin{align*} -\frac{\sqrt{-2 \, K r^{4} + 2 \, H r^{2} - a^{2}} x}{2 \, K r^{5} - 2 \, H r^{3} + a^{2} r} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.054584, size = 22, normalized size = 0.81 \begin{align*} \frac{x}{r \sqrt{2 H r^{2} - 2 K r^{4} - a^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05276, size = 34, normalized size = 1.26 \begin{align*} \frac{x}{\sqrt{-2 \, K r^{4} + 2 \, H r^{2} - a^{2}} r} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]