Optimal. Leaf size=29 \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.004519, antiderivative size = 29, 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 = {608, 31} \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 608
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{4-12 x+9 x^2}} \, dx &=\frac{(-6+9 x) \int \frac{1}{-6+9 x} \, dx}{\sqrt{4-12 x+9 x^2}}\\ &=-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{4-12 x+9 x^2}}\\ \end{align*}
Mathematica [A] time = 0.0107827, size = 26, normalized size = 0.9 \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{(2-3 x)^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.125, size = 23, normalized size = 0.8 \begin{align*}{\frac{ \left ( -2+3\,x \right ) \ln \left ( -2+3\,x \right ) }{3}{\frac{1}{\sqrt{ \left ( -2+3\,x \right ) ^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.67276, size = 8, normalized size = 0.28 \begin{align*} \frac{1}{3} \, \log \left (x - \frac{2}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.06614, size = 24, normalized size = 0.83 \begin{align*} \frac{1}{3} \, \log \left (3 \, x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.09535, size = 7, normalized size = 0.24 \begin{align*} \frac{\log{\left (3 x - 2 \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.62468, size = 20, normalized size = 0.69 \begin{align*} \frac{1}{3} \, \log \left ({\left | 3 \, x - 2 \right |}\right ) \mathrm{sgn}\left (3 \, x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]