Optimal. Leaf size=110 \[ \frac{\log \left (4 x^2-6 x+9\right )}{17496}+\frac{\log \left (4 x^2+6 x+9\right )}{17496}+\frac{1}{2916 (3-2 x)}-\frac{5 \log (3-2 x)}{17496}+\frac{\log (2 x+3)}{17496}-\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{2916 \sqrt{3}}+\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{8748 \sqrt{3}} \]
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Rubi [A] time = 0.206841, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 6, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.171 \[ \frac{\log \left (4 x^2-6 x+9\right )}{17496}+\frac{\log \left (4 x^2+6 x+9\right )}{17496}+\frac{1}{2916 (3-2 x)}-\frac{5 \log (3-2 x)}{17496}+\frac{\log (2 x+3)}{17496}-\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{2916 \sqrt{3}}+\frac{\tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{8748 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6)^2,x]
[Out]
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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((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729)**2,x)
[Out]
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Mathematica [A] time = 0.135762, size = 97, normalized size = 0.88 \[ \frac{3 \left (\log \left (4 x^2-6 x+9\right )+\log \left (4 x^2+6 x+9\right )+\frac{6}{3-2 x}-5 \log (3-2 x)+\log (2 x+3)\right )+6 \sqrt{3} \tan ^{-1}\left (\frac{4 x-3}{3 \sqrt{3}}\right )+2 \sqrt{3} \tan ^{-1}\left (\frac{4 x+3}{3 \sqrt{3}}\right )}{52488} \]
Antiderivative was successfully verified.
[In] Integrate[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6)^2,x]
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Maple [A] time = 0.015, size = 85, normalized size = 0.8 \[{\frac{\ln \left ( 2\,x+3 \right ) }{17496}}-{\frac{1}{-8748+5832\,x}}-{\frac{5\,\ln \left ( -3+2\,x \right ) }{17496}}+{\frac{\ln \left ( 4\,{x}^{2}+6\,x+9 \right ) }{17496}}+{\frac{\sqrt{3}}{26244}\arctan \left ({\frac{ \left ( 8\,x+6 \right ) \sqrt{3}}{18}} \right ) }+{\frac{\ln \left ( 4\,{x}^{2}-6\,x+9 \right ) }{17496}}+{\frac{\sqrt{3}}{8748}\arctan \left ({\frac{ \left ( 8\,x-6 \right ) \sqrt{3}}{18}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729)^2,x)
[Out]
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Maxima [A] time = 1.50101, size = 113, normalized size = 1.03 \[ \frac{1}{26244} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{1}{8748} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - \frac{1}{2916 \,{\left (2 \, x - 3\right )}} + \frac{1}{17496} \, \log \left (4 \, x^{2} + 6 \, x + 9\right ) + \frac{1}{17496} \, \log \left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{17496} \, \log \left (2 \, x + 3\right ) - \frac{5}{17496} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214526, size = 169, normalized size = 1.54 \[ \frac{\sqrt{3}{\left (\sqrt{3}{\left (2 \, x - 3\right )} \log \left (4 \, x^{2} + 6 \, x + 9\right ) + \sqrt{3}{\left (2 \, x - 3\right )} \log \left (4 \, x^{2} - 6 \, x + 9\right ) + \sqrt{3}{\left (2 \, x - 3\right )} \log \left (2 \, x + 3\right ) - 5 \, \sqrt{3}{\left (2 \, x - 3\right )} \log \left (2 \, x - 3\right ) + 2 \,{\left (2 \, x - 3\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + 6 \,{\left (2 \, x - 3\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - 6 \, \sqrt{3}\right )}}{52488 \,{\left (2 \, x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.593222, size = 105, normalized size = 0.95 \[ - \frac{5 \log{\left (x - \frac{3}{2} \right )}}{17496} + \frac{\log{\left (x + \frac{3}{2} \right )}}{17496} + \frac{\log{\left (x^{2} - \frac{3 x}{2} + \frac{9}{4} \right )}}{17496} + \frac{\log{\left (x^{2} + \frac{3 x}{2} + \frac{9}{4} \right )}}{17496} + \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right )}}{8748} + \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right )}}{26244} - \frac{1}{5832 x - 8748} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729)**2,x)
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GIAC/XCAS [A] time = 0.218703, size = 116, normalized size = 1.05 \[ \frac{1}{26244} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x + 3\right )}\right ) + \frac{1}{8748} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) - \frac{1}{2916 \,{\left (2 \, x - 3\right )}} + \frac{1}{17496} \,{\rm ln}\left (4 \, x^{2} + 6 \, x + 9\right ) + \frac{1}{17496} \,{\rm ln}\left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{17496} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - \frac{5}{17496} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729)^2,x, algorithm="giac")
[Out]