Optimal. Leaf size=13 \[ -\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0040812, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {619, 216} \[ -\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 619
Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{-2+5 x-3 x^2}} \, dx &=-\frac{\operatorname{Subst}\left (\int \frac{1}{\sqrt{1-x^2}} \, dx,x,5-6 x\right )}{\sqrt{3}}\\ &=-\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}}\\ \end{align*}
Mathematica [A] time = 0.0059762, size = 13, normalized size = 1. \[ -\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.057, size = 12, normalized size = 0.9 \begin{align*}{\frac{\arcsin \left ( -5+6\,x \right ) \sqrt{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.76947, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{3} \, \sqrt{3} \arcsin \left (6 \, x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.95196, size = 115, normalized size = 8.85 \begin{align*} -\frac{1}{3} \, \sqrt{3} \arctan \left (\frac{\sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x - 2}{\left (6 \, x - 5\right )}}{6 \,{\left (3 \, x^{2} - 5 \, x + 2\right )}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{- 3 x^{2} + 5 x - 2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.30049, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{3} \, \sqrt{3} \arcsin \left (6 \, x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]