Optimal. Leaf size=10 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0037278, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {1972, 216} \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1972
Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{(2-3 x) (2+3 x)}} \, dx &=\int \frac{1}{\sqrt{4-9 x^2}} \, dx\\ &=\frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right )\\ \end{align*}
Mathematica [A] time = 0.0040046, size = 10, normalized size = 1. \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 7, normalized size = 0.7 \begin{align*}{\frac{1}{3}\arcsin \left ({\frac{3\,x}{2}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.67563, size = 8, normalized size = 0.8 \begin{align*} \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.42755, size = 58, normalized size = 5.8 \begin{align*} -\frac{2}{3} \, \arctan \left (\frac{\sqrt{-9 \, x^{2} + 4} - 2}{3 \, x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.24983, size = 7, normalized size = 0.7 \begin{align*} \frac{\operatorname{asin}{\left (\frac{3 x}{2} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18089, size = 8, normalized size = 0.8 \begin{align*} \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]