Optimal. Leaf size=18 \[ -\frac{1}{3 x^3}-\frac{1}{x^2}-\frac{1}{x} \]
[Out]
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Rubi [A] time = 0.0153259, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{1}{3 x^3}-\frac{1}{x^2}-\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Int[(1 + 2*x + x^2)/x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.23781, size = 10, normalized size = 0.56 \[ - \frac{\left (x + 1\right )^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+2*x+1)/x**4,x)
[Out]
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Mathematica [A] time = 0.00157848, size = 18, normalized size = 1. \[ -\frac{1}{3 x^3}-\frac{1}{x^2}-\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 2*x + x^2)/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 17, normalized size = 0.9 \[ -{\frac{1}{3\,{x}^{3}}}-{x}^{-2}-{x}^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+2*x+1)/x^4,x)
[Out]
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Maxima [A] time = 0.799498, size = 20, normalized size = 1.11 \[ -\frac{3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198716, size = 20, normalized size = 1.11 \[ -\frac{3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.166582, size = 15, normalized size = 0.83 \[ - \frac{3 x^{2} + 3 x + 1}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+2*x+1)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.201347, size = 20, normalized size = 1.11 \[ -\frac{3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)/x^4,x, algorithm="giac")
[Out]