Optimal. Leaf size=69 \[ -\frac{502 x+313}{1452 \left (2 x^2+1\right )}+\frac{2843 \log \left (2 x^2+1\right )}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{503 \tan ^{-1}\left (\sqrt{2} x\right )}{7986 \sqrt{2}} \]
[Out]
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Rubi [A] time = 0.199109, antiderivative size = 86, normalized size of antiderivative = 1.25, number of steps used = 7, number of rules used = 5, integrand size = 50, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{502 x+313}{1452 \left (2 x^2+1\right )}+\frac{2843 \log \left (2 x^2+1\right )}{7986}+\frac{5828}{9075 (2-5 x)}-\frac{59096 \log (2-5 x)}{99825}+\frac{272 \sqrt{2} \tan ^{-1}\left (\sqrt{2} x\right )}{1331}-\frac{251 \tan ^{-1}\left (\sqrt{2} x\right )}{726 \sqrt{2}} \]
Antiderivative was successfully verified.
[In] Int[(8 - 13*x^2 - 7*x^3 + 12*x^5)/(4 - 20*x + 41*x^2 - 80*x^3 + 116*x^4 - 80*x^5 + 100*x^6),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((12*x**5-7*x**3-13*x**2+8)/(100*x**6-80*x**5+116*x**4-80*x**3+41*x**2-20*x+4),x)
[Out]
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Mathematica [A] time = 0.0749282, size = 67, normalized size = 0.97 \[ \frac{142150 \log \left (2 x^2+1\right )-\frac{33 \left (36458 x^2+4675 x+2554\right )}{10 x^3-4 x^2+5 x-2}-236384 \log (2-5 x)+12575 \sqrt{2} \tan ^{-1}\left (\sqrt{2} x\right )}{399300} \]
Antiderivative was successfully verified.
[In] Integrate[(8 - 13*x^2 - 7*x^3 + 12*x^5)/(4 - 20*x + 41*x^2 - 80*x^3 + 116*x^4 - 80*x^5 + 100*x^6),x]
[Out]
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Maple [A] time = 0.02, size = 54, normalized size = 0.8 \[{\frac{1}{3993} \left ( -{\frac{2761\,x}{4}}-{\frac{3443}{8}} \right ) \left ({x}^{2}+{\frac{1}{2}} \right ) ^{-1}}+{\frac{2843\,\ln \left ( 4\,{x}^{2}+2 \right ) }{7986}}+{\frac{503\,\arctan \left ( \sqrt{2}x \right ) \sqrt{2}}{15972}}-{\frac{5828}{45375\,x-18150}}-{\frac{59096\,\ln \left ( 5\,x-2 \right ) }{99825}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((12*x^5-7*x^3-13*x^2+8)/(100*x^6-80*x^5+116*x^4-80*x^3+41*x^2-20*x+4),x)
[Out]
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Maxima [A] time = 0.875479, size = 80, normalized size = 1.16 \[ \frac{503}{15972} \, \sqrt{2} \arctan \left (\sqrt{2} x\right ) - \frac{36458 \, x^{2} + 4675 \, x + 2554}{12100 \,{\left (10 \, x^{3} - 4 \, x^{2} + 5 \, x - 2\right )}} + \frac{2843}{7986} \, \log \left (2 \, x^{2} + 1\right ) - \frac{59096}{99825} \, \log \left (5 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((12*x^5 - 7*x^3 - 13*x^2 + 8)/(100*x^6 - 80*x^5 + 116*x^4 - 80*x^3 + 41*x^2 - 20*x + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.266174, size = 155, normalized size = 2.25 \[ \frac{\sqrt{2}{\left (142150 \, \sqrt{2}{\left (10 \, x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (2 \, x^{2} + 1\right ) - 236384 \, \sqrt{2}{\left (10 \, x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (5 \, x - 2\right ) + 25150 \,{\left (10 \, x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \arctan \left (\sqrt{2} x\right ) - 33 \, \sqrt{2}{\left (36458 \, x^{2} + 4675 \, x + 2554\right )}\right )}}{798600 \,{\left (10 \, x^{3} - 4 \, x^{2} + 5 \, x - 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((12*x^5 - 7*x^3 - 13*x^2 + 8)/(100*x^6 - 80*x^5 + 116*x^4 - 80*x^3 + 41*x^2 - 20*x + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.565926, size = 63, normalized size = 0.91 \[ - \frac{36458 x^{2} + 4675 x + 2554}{121000 x^{3} - 48400 x^{2} + 60500 x - 24200} - \frac{59096 \log{\left (x - \frac{2}{5} \right )}}{99825} + \frac{2843 \log{\left (x^{2} + \frac{1}{2} \right )}}{7986} + \frac{503 \sqrt{2} \operatorname{atan}{\left (\sqrt{2} x \right )}}{15972} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((12*x**5-7*x**3-13*x**2+8)/(100*x**6-80*x**5+116*x**4-80*x**3+41*x**2-20*x+4),x)
[Out]
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GIAC/XCAS [A] time = 0.26206, size = 80, normalized size = 1.16 \[ \frac{503}{15972} \, \sqrt{2} \arctan \left (\sqrt{2} x\right ) - \frac{36458 \, x^{2} + 4675 \, x + 2554}{12100 \,{\left (2 \, x^{2} + 1\right )}{\left (5 \, x - 2\right )}} + \frac{2843}{7986} \,{\rm ln}\left (2 \, x^{2} + 1\right ) - \frac{59096}{99825} \,{\rm ln}\left ({\left | 5 \, x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((12*x^5 - 7*x^3 - 13*x^2 + 8)/(100*x^6 - 80*x^5 + 116*x^4 - 80*x^3 + 41*x^2 - 20*x + 4),x, algorithm="giac")
[Out]