Optimal. Leaf size=15 \[ -\frac{1}{4} \sqrt{9-4 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.002276, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ -\frac{1}{4} \sqrt{9-4 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{9-4 x^2}} \, dx &=-\frac{1}{4} \sqrt{9-4 x^2}\\ \end{align*}
Mathematica [A] time = 0.0013072, size = 15, normalized size = 1. \[ -\frac{1}{4} \sqrt{9-4 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 22, normalized size = 1.5 \begin{align*}{\frac{ \left ( -3+2\,x \right ) \left ( 3+2\,x \right ) }{4}{\frac{1}{\sqrt{-4\,{x}^{2}+9}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.50057, size = 15, normalized size = 1. \begin{align*} -\frac{1}{4} \, \sqrt{-4 \, x^{2} + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.19692, size = 31, normalized size = 2.07 \begin{align*} -\frac{1}{4} \, \sqrt{-4 \, x^{2} + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.135019, size = 12, normalized size = 0.8 \begin{align*} - \frac{\sqrt{9 - 4 x^{2}}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.81202, size = 15, normalized size = 1. \begin{align*} -\frac{1}{4} \, \sqrt{-4 \, x^{2} + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]