Optimal. Leaf size=42 \[ -\frac{5-6 x}{49 \left (-3 x^2+5 x+2\right )}-\frac{6}{343} \log (2-x)+\frac{6}{343} \log (3 x+1) \]
[Out]
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Rubi [A] time = 0.0260591, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{5-6 x}{49 \left (-3 x^2+5 x+2\right )}-\frac{6}{343} \log (2-x)+\frac{6}{343} \log (3 x+1) \]
Antiderivative was successfully verified.
[In] Int[(2 + 5*x - 3*x^2)^(-2),x]
[Out]
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Rubi in Sympy [A] time = 2.1557, size = 32, normalized size = 0.76 \[ - \frac{- 6 x + 5}{49 \left (- 3 x^{2} + 5 x + 2\right )} - \frac{6 \log{\left (- x + 2 \right )}}{343} + \frac{6 \log{\left (3 x + 1 \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3*x**2+5*x+2)**2,x)
[Out]
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Mathematica [A] time = 0.0231421, size = 42, normalized size = 1. \[ \frac{5-6 x}{49 \left (3 x^2-5 x-2\right )}-\frac{6}{343} \log (2-x)+\frac{6}{343} \log (3 x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 5*x - 3*x^2)^(-2),x]
[Out]
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Maple [A] time = 0.013, size = 32, normalized size = 0.8 \[ -{\frac{3}{147\,x+49}}+{\frac{6\,\ln \left ( 3\,x+1 \right ) }{343}}-{\frac{1}{49\,x-98}}-{\frac{6\,\ln \left ( x-2 \right ) }{343}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3*x^2+5*x+2)^2,x)
[Out]
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Maxima [A] time = 0.715969, size = 46, normalized size = 1.1 \[ -\frac{6 \, x - 5}{49 \,{\left (3 \, x^{2} - 5 \, x - 2\right )}} + \frac{6}{343} \, \log \left (3 \, x + 1\right ) - \frac{6}{343} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 5*x - 2)^(-2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21972, size = 72, normalized size = 1.71 \[ \frac{6 \,{\left (3 \, x^{2} - 5 \, x - 2\right )} \log \left (3 \, x + 1\right ) - 6 \,{\left (3 \, x^{2} - 5 \, x - 2\right )} \log \left (x - 2\right ) - 42 \, x + 35}{343 \,{\left (3 \, x^{2} - 5 \, x - 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 5*x - 2)^(-2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.324176, size = 32, normalized size = 0.76 \[ - \frac{6 x - 5}{147 x^{2} - 245 x - 98} - \frac{6 \log{\left (x - 2 \right )}}{343} + \frac{6 \log{\left (x + \frac{1}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3*x**2+5*x+2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209558, size = 49, normalized size = 1.17 \[ -\frac{6 \, x - 5}{49 \,{\left (3 \, x^{2} - 5 \, x - 2\right )}} + \frac{6}{343} \,{\rm ln}\left ({\left | 3 \, x + 1 \right |}\right ) - \frac{6}{343} \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 5*x - 2)^(-2),x, algorithm="giac")
[Out]