Optimal. Leaf size=24 \[ -\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{3 \sqrt{3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0237435, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.12, Rules used = {1586, 618, 204} \[ -\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{3 \sqrt{3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1586
Rule 618
Rule 204
Rubi steps
\begin{align*} \int \frac{81+54 x-24 x^3-16 x^4}{729-64 x^6} \, dx &=\int \frac{1}{9-6 x+4 x^2} \, dx\\ &=-\left (2 \operatorname{Subst}\left (\int \frac{1}{-108-x^2} \, dx,x,-6+8 x\right )\right )\\ &=-\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{3 \sqrt{3}}\\ \end{align*}
Mathematica [A] time = 0.0063597, size = 24, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{4 x-3}{3 \sqrt{3}}\right )}{3 \sqrt{3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 17, normalized size = 0.7 \begin{align*}{\frac{\sqrt{3}}{9}\arctan \left ({\frac{ \left ( 8\,x-6 \right ) \sqrt{3}}{18}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.37219, size = 22, normalized size = 0.92 \begin{align*} \frac{1}{9} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.35482, size = 58, normalized size = 2.42 \begin{align*} \frac{1}{9} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.114066, size = 24, normalized size = 1. \begin{align*} \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right )}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05202, size = 22, normalized size = 0.92 \begin{align*} \frac{1}{9} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]