Optimal. Leaf size=88 \[ \frac{\log \left (\frac{2 \sqrt [3]{2} \sqrt [3]{3 x^2-6 x+4}+2 x-4}{x}\right )}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left (\frac{-2 \sqrt [3]{2} \sqrt [3]{3 x^2-6 x+4}+x-2}{\sqrt{3} (x-2)}\right )}{2^{2/3} \sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0472327, antiderivative size = 97, normalized size of antiderivative = 1.1, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{\log \left (-3 \sqrt [3]{2} \sqrt [3]{3 x^2-6 x+4}-3 x+6\right )}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left (\frac{2^{2/3} (2-x)}{\sqrt{3} \sqrt [3]{3 x^2-6 x+4}}+\frac{1}{\sqrt{3}}\right )}{2^{2/3} \sqrt{3}}-\frac{\log (x)}{2\ 2^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.41973, size = 94, normalized size = 1.07 \[ - \frac{\sqrt [3]{2} \log{\left (x \right )}}{4} + \frac{\sqrt [3]{2} \log{\left (- 3 x - 3 \sqrt [3]{2} \sqrt [3]{3 x^{2} - 6 x + 4} + 6 \right )}}{4} - \frac{\sqrt [3]{2} \sqrt{3} \operatorname{atan}{\left (\frac{2^{\frac{2}{3}} \sqrt{3} \left (- 3 x + 6\right )}{9 \sqrt [3]{3 x^{2} - 6 x + 4}} + \frac{\sqrt{3}}{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(3*x**2-6*x+4)**(1/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.810162, size = 273, normalized size = 3.1 \[ -\frac{15 x \left (3 x-i \sqrt{3}-3\right ) \left (3 x+i \sqrt{3}-3\right ) F_1\left (\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right )}{2 \left (3 x^2-6 x+4\right )^{4/3} \left (15 x F_1\left (\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right )+\left (3+i \sqrt{3}\right ) F_1\left (\frac{5}{3};\frac{1}{3},\frac{4}{3};\frac{8}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right )+\left (3-i \sqrt{3}\right ) F_1\left (\frac{5}{3};\frac{4}{3},\frac{1}{3};\frac{8}{3};\frac{3-i \sqrt{3}}{3 x},\frac{3+i \sqrt{3}}{3 x}\right )\right )} \]
Warning: Unable to verify antiderivative.
[In] Integrate[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.199, size = 0, normalized size = 0. \[ \int{\frac{1}{x}{\frac{1}{\sqrt [3]{3\,{x}^{2}-6\,x+4}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(3*x^2-6*x+4)^(1/3),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (3 \, x^{2} - 6 \, x + 4\right )}^{\frac{1}{3}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^2 - 6*x + 4)^(1/3)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^2 - 6*x + 4)^(1/3)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt [3]{3 x^{2} - 6 x + 4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(3*x**2-6*x+4)**(1/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (3 \, x^{2} - 6 \, x + 4\right )}^{\frac{1}{3}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((3*x^2 - 6*x + 4)^(1/3)*x),x, algorithm="giac")
[Out]