Optimal. Leaf size=33 \[ \frac{7}{4} \log \left (x^2-8 x+21\right )-\frac{13 \tan ^{-1}\left (\frac{4-x}{\sqrt{5}}\right )}{\sqrt{5}} \]
[Out]
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Rubi [A] time = 0.0445784, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{7}{4} \log \left (x^2-8 x+21\right )-\frac{13 \tan ^{-1}\left (\frac{4-x}{\sqrt{5}}\right )}{\sqrt{5}} \]
Antiderivative was successfully verified.
[In] Int[(-2 + 7*x)/(42 - 16*x + 2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 6.20976, size = 36, normalized size = 1.09 \[ \frac{7 \log{\left (2 x^{2} - 16 x + 42 \right )}}{4} + \frac{13 \sqrt{5} \operatorname{atan}{\left (\sqrt{5} \left (\frac{x}{5} - \frac{4}{5}\right ) \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-2+7*x)/(2*x**2-16*x+42),x)
[Out]
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Mathematica [A] time = 0.0203154, size = 35, normalized size = 1.06 \[ \frac{1}{2} \left (\frac{7}{2} \log \left (x^2-8 x+21\right )+\frac{26 \tan ^{-1}\left (\frac{x-4}{\sqrt{5}}\right )}{\sqrt{5}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-2 + 7*x)/(42 - 16*x + 2*x^2),x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 0.9 \[{\frac{7\,\ln \left ({x}^{2}-8\,x+21 \right ) }{4}}+{\frac{13\,\sqrt{5}}{5}\arctan \left ({\frac{ \left ( 2\,x-8 \right ) \sqrt{5}}{10}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-2+7*x)/(2*x^2-16*x+42),x)
[Out]
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Maxima [A] time = 0.766753, size = 35, normalized size = 1.06 \[ \frac{13}{5} \, \sqrt{5} \arctan \left (\frac{1}{5} \, \sqrt{5}{\left (x - 4\right )}\right ) + \frac{7}{4} \, \log \left (x^{2} - 8 \, x + 21\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2*(7*x - 2)/(x^2 - 8*x + 21),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270567, size = 42, normalized size = 1.27 \[ \frac{1}{20} \, \sqrt{5}{\left (7 \, \sqrt{5} \log \left (x^{2} - 8 \, x + 21\right ) + 52 \, \arctan \left (\frac{1}{5} \, \sqrt{5}{\left (x - 4\right )}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2*(7*x - 2)/(x^2 - 8*x + 21),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.252927, size = 39, normalized size = 1.18 \[ \frac{7 \log{\left (x^{2} - 8 x + 21 \right )}}{4} + \frac{13 \sqrt{5} \operatorname{atan}{\left (\frac{\sqrt{5} x}{5} - \frac{4 \sqrt{5}}{5} \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2+7*x)/(2*x**2-16*x+42),x)
[Out]
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GIAC/XCAS [A] time = 0.273285, size = 35, normalized size = 1.06 \[ \frac{13}{5} \, \sqrt{5} \arctan \left (\frac{1}{5} \, \sqrt{5}{\left (x - 4\right )}\right ) + \frac{7}{4} \,{\rm ln}\left (x^{2} - 8 \, x + 21\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2*(7*x - 2)/(x^2 - 8*x + 21),x, algorithm="giac")
[Out]