Optimal. Leaf size=113 \[ \frac{x}{4374 \left (8 x^3+27\right )}-\frac{7 \log \left (4 x^2-6 x+9\right )}{944784}+\frac{\log \left (4 x^2+6 x+9\right )}{314928}-\frac{\log (3-2 x)}{157464}+\frac{7 \log (2 x+3)}{472392}-\frac{7 \tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{52488 \sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.167001, antiderivative size = 113, normalized size of antiderivative = 1., number of steps used = 15, number of rules used = 9, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.529 \[ \frac{x}{4374 \left (8 x^3+27\right )}-\frac{7 \log \left (4 x^2-6 x+9\right )}{944784}+\frac{\log \left (4 x^2+6 x+9\right )}{314928}-\frac{\log (3-2 x)}{157464}+\frac{7 \log (2 x+3)}{472392}-\frac{7 \tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{52488 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(27 - 8*x^3)/(729 - 64*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 25.8493, size = 100, normalized size = 0.88 \[ \frac{x}{4374 \left (8 x^{3} + 27\right )} - \frac{\log{\left (- 2 x + 3 \right )}}{157464} + \frac{7 \log{\left (2 x + 3 \right )}}{472392} - \frac{7 \log{\left (4 x^{2} - 6 x + 9 \right )}}{944784} + \frac{\log{\left (4 x^{2} + 6 x + 9 \right )}}{314928} + \frac{7 \sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{4 x}{9} - \frac{1}{3}\right ) \right )}}{472392} + \frac{\sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{4 x}{9} + \frac{1}{3}\right ) \right )}}{157464} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-8*x**3+27)/(-64*x**6+729)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0930914, size = 103, normalized size = 0.91 \[ \frac{\frac{216 x}{8 x^3+27}-7 \log \left (4 x^2-6 x+9\right )+3 \log \left (4 x^2+6 x+9\right )-6 \log (3-2 x)+14 \log (2 x+3)+14 \sqrt{3} \tan ^{-1}\left (\frac{4 x-3}{3 \sqrt{3}}\right )+6 \sqrt{3} \tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{944784} \]
Antiderivative was successfully verified.
[In] Integrate[(27 - 8*x^3)/(729 - 64*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.019, size = 102, normalized size = 0.9 \[ -{\frac{1}{157464\,x+236196}}+{\frac{7\,\ln \left ( 2\,x+3 \right ) }{472392}}-{\frac{\ln \left ( -3+2\,x \right ) }{157464}}+{\frac{\ln \left ( 4\,{x}^{2}+6\,x+9 \right ) }{314928}}+{\frac{\sqrt{3}}{157464}\arctan \left ({\frac{ \left ( 8\,x+6 \right ) \sqrt{3}}{18}} \right ) }-{\frac{1}{118098} \left ( -{\frac{3\,x}{4}}-{\frac{9}{8}} \right ) \left ({x}^{2}-{\frac{3\,x}{2}}+{\frac{9}{4}} \right ) ^{-1}}-{\frac{7\,\ln \left ( 16\,{x}^{2}-24\,x+36 \right ) }{944784}}+{\frac{7\,\sqrt{3}}{472392}\arctan \left ({\frac{ \left ( 32\,x-24 \right ) \sqrt{3}}{72}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-8*x^3+27)/(-64*x^6+729)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.52106, size = 117, normalized size = 1.04 \[ \frac{1}{157464} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{7}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + \frac{x}{4374 \,{\left (8 \, x^{3} + 27\right )}} + \frac{1}{314928} \, \log \left (4 \, x^{2} + 6 \, x + 9\right ) - \frac{7}{944784} \, \log \left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{7}{472392} \, \log \left (2 \, x + 3\right ) - \frac{1}{157464} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(8*x^3 - 27)/(64*x^6 - 729)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21153, size = 193, normalized size = 1.71 \[ \frac{\sqrt{3}{\left (3 \, \sqrt{3}{\left (8 \, x^{3} + 27\right )} \log \left (4 \, x^{2} + 6 \, x + 9\right ) - 7 \, \sqrt{3}{\left (8 \, x^{3} + 27\right )} \log \left (4 \, x^{2} - 6 \, x + 9\right ) + 14 \, \sqrt{3}{\left (8 \, x^{3} + 27\right )} \log \left (2 \, x + 3\right ) - 6 \, \sqrt{3}{\left (8 \, x^{3} + 27\right )} \log \left (2 \, x - 3\right ) + 18 \,{\left (8 \, x^{3} + 27\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + 42 \,{\left (8 \, x^{3} + 27\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + 216 \, \sqrt{3} x\right )}}{2834352 \,{\left (8 \, x^{3} + 27\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(8*x^3 - 27)/(64*x^6 - 729)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.679236, size = 110, normalized size = 0.97 \[ \frac{x}{34992 x^{3} + 118098} - \frac{\log{\left (x - \frac{3}{2} \right )}}{157464} + \frac{7 \log{\left (x + \frac{3}{2} \right )}}{472392} - \frac{7 \log{\left (x^{2} - \frac{3 x}{2} + \frac{9}{4} \right )}}{944784} + \frac{\log{\left (x^{2} + \frac{3 x}{2} + \frac{9}{4} \right )}}{314928} + \frac{7 \sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right )}}{472392} + \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right )}}{157464} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-8*x**3+27)/(-64*x**6+729)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.219819, size = 120, normalized size = 1.06 \[ \frac{1}{157464} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{7}{472392} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + \frac{x}{4374 \,{\left (8 \, x^{3} + 27\right )}} + \frac{1}{314928} \,{\rm ln}\left (4 \, x^{2} + 6 \, x + 9\right ) - \frac{7}{944784} \,{\rm ln}\left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{7}{472392} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - \frac{1}{157464} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(8*x^3 - 27)/(64*x^6 - 729)^2,x, algorithm="giac")
[Out]