Optimal. Leaf size=131 \[ -\frac{3-2 x}{26244 \left (4 x^2-6 x+9\right )}+\frac{17 \log \left (4 x^2-6 x+9\right )}{944784}+\frac{\log \left (4 x^2+6 x+9\right )}{314928}+\frac{1}{26244 (3-2 x)}-\frac{7 \log (3-2 x)}{157464}+\frac{\log (2 x+3)}{472392}-\frac{11 \tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{157464 \sqrt{3}}-\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{157464 \sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.263878, antiderivative size = 131, normalized size of antiderivative = 1., number of steps used = 14, number of rules used = 7, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.28 \[ -\frac{3-2 x}{26244 \left (4 x^2-6 x+9\right )}+\frac{17 \log \left (4 x^2-6 x+9\right )}{944784}+\frac{\log \left (4 x^2+6 x+9\right )}{314928}+\frac{1}{26244 (3-2 x)}-\frac{7 \log (3-2 x)}{157464}+\frac{\log (2 x+3)}{472392}-\frac{11 \tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{157464 \sqrt{3}}-\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{157464 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((8*x**3+24*x**2+36*x+27)/(-64*x**6+729)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.110413, size = 111, normalized size = 0.85 \[ \frac{17 \log \left (4 x^2-6 x+9\right )+3 \log \left (4 x^2+6 x+9\right )+\frac{216 x}{-8 x^3+24 x^2-36 x+27}-42 \log (3-2 x)+2 \log (2 x+3)+22 \sqrt{3} \tan ^{-1}\left (\frac{4 x-3}{3 \sqrt{3}}\right )-2 \sqrt{3} \tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{944784} \]
Antiderivative was successfully verified.
[In] Integrate[(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.019, size = 102, normalized size = 0.8 \[{\frac{\ln \left ( 2\,x+3 \right ) }{472392}}-{\frac{1}{-78732+52488\,x}}-{\frac{7\,\ln \left ( -3+2\,x \right ) }{157464}}+{\frac{\ln \left ( 4\,{x}^{2}+6\,x+9 \right ) }{314928}}-{\frac{\sqrt{3}}{472392}\arctan \left ({\frac{ \left ( 8\,x+6 \right ) \sqrt{3}}{18}} \right ) }+{\frac{1}{118098} \left ({\frac{9\,x}{4}}-{\frac{27}{8}} \right ) \left ({x}^{2}-{\frac{3\,x}{2}}+{\frac{9}{4}} \right ) ^{-1}}+{\frac{17\,\ln \left ( 16\,{x}^{2}-24\,x+36 \right ) }{944784}}+{\frac{11\,\sqrt{3}}{472392}\arctan \left ({\frac{ \left ( 32\,x-24 \right ) \sqrt{3}}{72}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((8*x^3+24*x^2+36*x+27)/(-64*x^6+729)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.54312, size = 128, normalized size = 0.98 \[ -\frac{1}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{11}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - \frac{x}{4374 \,{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )}} + \frac{1}{314928} \, \log \left (4 \, x^{2} + 6 \, x + 9\right ) + \frac{17}{944784} \, \log \left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{472392} \, \log \left (2 \, x + 3\right ) - \frac{7}{157464} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 24*x^2 + 36*x + 27)/(64*x^6 - 729)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.213829, size = 269, normalized size = 2.05 \[ \frac{\sqrt{3}{\left (3 \, \sqrt{3}{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \log \left (4 \, x^{2} + 6 \, x + 9\right ) + 17 \, \sqrt{3}{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \log \left (4 \, x^{2} - 6 \, x + 9\right ) + 2 \, \sqrt{3}{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \log \left (2 \, x + 3\right ) - 42 \, \sqrt{3}{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \log \left (2 \, x - 3\right ) - 6 \,{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + 66 \,{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - 216 \, \sqrt{3} x\right )}}{2834352 \,{\left (8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 24*x^2 + 36*x + 27)/(64*x^6 - 729)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.82442, size = 119, normalized size = 0.91 \[ - \frac{x}{34992 x^{3} - 104976 x^{2} + 157464 x - 118098} - \frac{7 \log{\left (x - \frac{3}{2} \right )}}{157464} + \frac{\log{\left (x + \frac{3}{2} \right )}}{472392} + \frac{17 \log{\left (x^{2} - \frac{3 x}{2} + \frac{9}{4} \right )}}{944784} + \frac{\log{\left (x^{2} + \frac{3 x}{2} + \frac{9}{4} \right )}}{314928} + \frac{11 \sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right )}}{472392} - \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right )}}{472392} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x**3+24*x**2+36*x+27)/(-64*x**6+729)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.219799, size = 134, normalized size = 1.02 \[ -\frac{1}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{11}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - \frac{x}{4374 \,{\left (4 \, x^{2} - 6 \, x + 9\right )}{\left (2 \, x - 3\right )}} + \frac{1}{314928} \,{\rm ln}\left (4 \, x^{2} + 6 \, x + 9\right ) + \frac{17}{944784} \,{\rm ln}\left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{472392} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - \frac{7}{157464} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 24*x^2 + 36*x + 27)/(64*x^6 - 729)^2,x, algorithm="giac")
[Out]