Optimal. Leaf size=92 \[ \frac{x}{4374 \left (4 x^2-6 x+9\right )}-\frac{\log \left (4 x^2-6 x+9\right )}{157464}+\frac{\log \left (4 x^2+6 x+9\right )}{52488}-\frac{\log (3-2 x)}{26244}+\frac{\log (2 x+3)}{78732}-\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{4374 \sqrt{3}} \]
[Out]
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Rubi [A] time = 0.207291, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 7, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.28 \[ \frac{x}{4374 \left (4 x^2-6 x+9\right )}-\frac{\log \left (4 x^2-6 x+9\right )}{157464}+\frac{\log \left (4 x^2+6 x+9\right )}{52488}-\frac{\log (3-2 x)}{26244}+\frac{\log (2 x+3)}{78732}-\frac{\tan ^{-1}\left (\frac{3-4 x}{3 \sqrt{3}}\right )}{4374 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(81 + 54*x - 24*x^3 - 16*x^4)/(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((-16*x**4-24*x**3+54*x+81)/(-64*x**6+729)**2,x)
[Out]
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Mathematica [A] time = 0.0593725, size = 84, normalized size = 0.91 \[ \frac{\frac{36 x}{4 x^2-6 x+9}-\log \left (4 x^2-6 x+9\right )+3 \log \left (4 x^2+6 x+9\right )-6 \log (3-2 x)+2 \log (2 x+3)+12 \sqrt{3} \tan ^{-1}\left (\frac{4 x-3}{3 \sqrt{3}}\right )}{157464} \]
Antiderivative was successfully verified.
[In] Integrate[(81 + 54*x - 24*x^3 - 16*x^4)/(729 - 64*x^6)^2,x]
[Out]
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Maple [A] time = 0.019, size = 73, normalized size = 0.8 \[{\frac{\ln \left ( 2\,x+3 \right ) }{78732}}-{\frac{\ln \left ( -3+2\,x \right ) }{26244}}+{\frac{\ln \left ( 4\,{x}^{2}+6\,x+9 \right ) }{52488}}+{\frac{x}{17496} \left ({x}^{2}-{\frac{3\,x}{2}}+{\frac{9}{4}} \right ) ^{-1}}-{\frac{\ln \left ( 16\,{x}^{2}-24\,x+36 \right ) }{157464}}+{\frac{\sqrt{3}}{13122}\arctan \left ({\frac{ \left ( 32\,x-24 \right ) \sqrt{3}}{72}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729)^2,x)
[Out]
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Maxima [A] time = 1.58063, size = 100, normalized size = 1.09 \[ \frac{1}{13122} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + \frac{x}{4374 \,{\left (4 \, x^{2} - 6 \, x + 9\right )}} + \frac{1}{52488} \, \log \left (4 \, x^{2} + 6 \, x + 9\right ) - \frac{1}{157464} \, \log \left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{78732} \, \log \left (2 \, x + 3\right ) - \frac{1}{26244} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^4 + 24*x^3 - 54*x - 81)/(64*x^6 - 729)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21308, size = 190, normalized size = 2.07 \[ \frac{\sqrt{3}{\left (3 \, \sqrt{3}{\left (4 \, x^{2} - 6 \, x + 9\right )} \log \left (4 \, x^{2} + 6 \, x + 9\right ) - \sqrt{3}{\left (4 \, x^{2} - 6 \, x + 9\right )} \log \left (4 \, x^{2} - 6 \, x + 9\right ) + 2 \, \sqrt{3}{\left (4 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x + 3\right ) - 6 \, \sqrt{3}{\left (4 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 3\right ) + 36 \,{\left (4 \, x^{2} - 6 \, x + 9\right )} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + 36 \, \sqrt{3} x\right )}}{472392 \,{\left (4 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^4 + 24*x^3 - 54*x - 81)/(64*x^6 - 729)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.462992, size = 82, normalized size = 0.89 \[ \frac{x}{17496 x^{2} - 26244 x + 39366} - \frac{\log{\left (x - \frac{3}{2} \right )}}{26244} + \frac{\log{\left (x + \frac{3}{2} \right )}}{78732} - \frac{\log{\left (x^{2} - \frac{3 x}{2} + \frac{9}{4} \right )}}{157464} + \frac{\log{\left (4 x^{2} + 6 x + 9 \right )}}{52488} + \frac{\sqrt{3} \operatorname{atan}{\left (\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right )}}{13122} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-16*x**4-24*x**3+54*x+81)/(-64*x**6+729)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219609, size = 103, normalized size = 1.12 \[ \frac{1}{13122} \, \sqrt{3} \arctan \left (\frac{1}{9} \, \sqrt{3}{\left (4 \, x - 3\right )}\right ) + \frac{x}{4374 \,{\left (4 \, x^{2} - 6 \, x + 9\right )}} + \frac{1}{52488} \,{\rm ln}\left (4 \, x^{2} + 6 \, x + 9\right ) - \frac{1}{157464} \,{\rm ln}\left (4 \, x^{2} - 6 \, x + 9\right ) + \frac{1}{78732} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - \frac{1}{26244} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^4 + 24*x^3 - 54*x - 81)/(64*x^6 - 729)^2,x, algorithm="giac")
[Out]