Optimal. Leaf size=19 \[ \frac{1}{x+1}-\frac{1}{(x+1)^2}+2 \log (x+1) \]
[Out]
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Rubi [A] time = 0.0301152, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{x+1}-\frac{1}{(x+1)^2}+2 \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(3 + 3*x + 2*x^2)/(1 + x)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.19602, size = 17, normalized size = 0.89 \[ 2 \log{\left (x + 1 \right )} + \frac{1}{x + 1} - \frac{1}{\left (x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**2+3*x+3)/(1+x)**3,x)
[Out]
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Mathematica [A] time = 0.0149365, size = 19, normalized size = 1. \[ \frac{1}{x+1}-\frac{1}{(x+1)^2}+2 \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 3*x + 2*x^2)/(1 + x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 20, normalized size = 1.1 \[ - \left ( 1+x \right ) ^{-2}+ \left ( 1+x \right ) ^{-1}+2\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^2+3*x+3)/(1+x)^3,x)
[Out]
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Maxima [A] time = 0.793498, size = 26, normalized size = 1.37 \[ \frac{x}{x^{2} + 2 \, x + 1} + 2 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 3*x + 3)/(x + 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213295, size = 36, normalized size = 1.89 \[ \frac{2 \,{\left (x^{2} + 2 \, x + 1\right )} \log \left (x + 1\right ) + x}{x^{2} + 2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 3*x + 3)/(x + 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.206183, size = 15, normalized size = 0.79 \[ \frac{x}{x^{2} + 2 x + 1} + 2 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**2+3*x+3)/(1+x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.203072, size = 20, normalized size = 1.05 \[ \frac{x}{{\left (x + 1\right )}^{2}} + 2 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 3*x + 3)/(x + 1)^3,x, algorithm="giac")
[Out]