Optimal. Leaf size=15 \[ \frac{1}{1-x}-\frac{2}{(x+1)^2} \]
[Out]
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Rubi [A] time = 0.0370854, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{1}{1-x}-\frac{2}{(x+1)^2} \]
Antiderivative was successfully verified.
[In] Int[(5 - 5*x + 7*x^2 + x^3)/((-1 + x)^2*(1 + x)^3),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((x**3+7*x**2-5*x+5)/(-1+x)**2/(1+x)**3,x)
[Out]
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Mathematica [A] time = 0.0191993, size = 15, normalized size = 1. \[ -\frac{2}{(x+1)^2}-\frac{1}{x-1} \]
Antiderivative was successfully verified.
[In] Integrate[(5 - 5*x + 7*x^2 + x^3)/((-1 + x)^2*(1 + x)^3),x]
[Out]
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Maple [A] time = 0.008, size = 16, normalized size = 1.1 \[ - \left ( -1+x \right ) ^{-1}-2\, \left ( 1+x \right ) ^{-2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3+7*x^2-5*x+5)/(-1+x)^2/(1+x)^3,x)
[Out]
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Maxima [A] time = 0.797168, size = 31, normalized size = 2.07 \[ -\frac{x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 7*x^2 - 5*x + 5)/((x + 1)^3*(x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242329, size = 31, normalized size = 2.07 \[ -\frac{x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 7*x^2 - 5*x + 5)/((x + 1)^3*(x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.274454, size = 19, normalized size = 1.27 \[ - \frac{x^{2} + 4 x - 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3+7*x**2-5*x+5)/(-1+x)**2/(1+x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.262833, size = 41, normalized size = 2.73 \[ -\frac{1}{x - 1} + \frac{\frac{4}{x - 1} + 1}{2 \,{\left (\frac{2}{x - 1} + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + 7*x^2 - 5*x + 5)/((x + 1)^3*(x - 1)^2),x, algorithm="giac")
[Out]