Optimal. Leaf size=47 \[ -\frac{1}{6} \left (9-5 \sqrt{6}\right ) \log \left (x-\sqrt{6}+1\right )-\frac{1}{6} \left (9+5 \sqrt{6}\right ) \log \left (x+\sqrt{6}+1\right ) \]
[Out]
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Rubi [A] time = 0.0700014, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{1}{6} \left (9-5 \sqrt{6}\right ) \log \left (x-\sqrt{6}+1\right )-\frac{1}{6} \left (9+5 \sqrt{6}\right ) \log \left (x+\sqrt{6}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(7 - 3*x)/(-5 + 2*x + x^2),x]
[Out]
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Rubi in Sympy [A] time = 4.69202, size = 49, normalized size = 1.04 \[ - \frac{\sqrt{6} \left (3 \sqrt{6} + 10\right ) \log{\left (x + 1 + \sqrt{6} \right )}}{12} + \frac{\sqrt{6} \left (- 3 \sqrt{6} + 10\right ) \log{\left (x - \sqrt{6} + 1 \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((7-3*x)/(x**2+2*x-5),x)
[Out]
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Mathematica [A] time = 0.0646039, size = 47, normalized size = 1. \[ \frac{1}{6} \left (5 \sqrt{6}-9\right ) \log \left (-x+\sqrt{6}-1\right )+\frac{1}{6} \left (-9-5 \sqrt{6}\right ) \log \left (x+\sqrt{6}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(7 - 3*x)/(-5 + 2*x + x^2),x]
[Out]
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Maple [A] time = 0.005, size = 29, normalized size = 0.6 \[ -{\frac{3\,\ln \left ({x}^{2}+2\,x-5 \right ) }{2}}-{\frac{5\,\sqrt{6}}{3}{\it Artanh} \left ({\frac{ \left ( 2+2\,x \right ) \sqrt{6}}{12}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((7-3*x)/(x^2+2*x-5),x)
[Out]
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Maxima [A] time = 0.912049, size = 47, normalized size = 1. \[ \frac{5}{6} \, \sqrt{6} \log \left (\frac{x - \sqrt{6} + 1}{x + \sqrt{6} + 1}\right ) - \frac{3}{2} \, \log \left (x^{2} + 2 \, x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x - 7)/(x^2 + 2*x - 5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220895, size = 78, normalized size = 1.66 \[ -\frac{1}{6} \, \sqrt{3}{\left (3 \, \sqrt{3} \log \left (x^{2} + 2 \, x - 5\right ) - 5 \, \sqrt{2} \log \left (\frac{\sqrt{3}{\left (x^{2} + 2 \, x + 7\right )} - 6 \, \sqrt{2}{\left (x + 1\right )}}{x^{2} + 2 \, x - 5}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x - 7)/(x^2 + 2*x - 5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.242424, size = 44, normalized size = 0.94 \[ - \left (\frac{3}{2} + \frac{5 \sqrt{6}}{6}\right ) \log{\left (x + 1 + \sqrt{6} \right )} - \left (- \frac{5 \sqrt{6}}{6} + \frac{3}{2}\right ) \log{\left (x - \sqrt{6} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((7-3*x)/(x**2+2*x-5),x)
[Out]
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GIAC/XCAS [A] time = 0.203772, size = 59, normalized size = 1.26 \[ \frac{5}{6} \, \sqrt{6}{\rm ln}\left (\frac{{\left | 2 \, x - 2 \, \sqrt{6} + 2 \right |}}{{\left | 2 \, x + 2 \, \sqrt{6} + 2 \right |}}\right ) - \frac{3}{2} \,{\rm ln}\left ({\left | x^{2} + 2 \, x - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x - 7)/(x^2 + 2*x - 5),x, algorithm="giac")
[Out]