Optimal. Leaf size=13 \[ -\frac{1}{4 \left ((x+2)^2+1\right )^2} \]
[Out]
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Rubi [A] time = 0.00808053, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{4 \left ((x+2)^2+1\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(2 + x)/(1 + (2 + x)^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 2.17161, size = 12, normalized size = 0.92 \[ - \frac{1}{4 \left (\left (x + 2\right )^{2} + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+x)/(1+(2+x)**2)**3,x)
[Out]
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Mathematica [A] time = 0.00441033, size = 13, normalized size = 1. \[ -\frac{1}{4 \left ((x+2)^2+1\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + x)/(1 + (2 + x)^2)^3,x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 1. \[ -{\frac{1}{4\, \left ({x}^{2}+4\,x+5 \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+x)/(1+(2+x)^2)^3,x)
[Out]
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Maxima [A] time = 1.42362, size = 15, normalized size = 1.15 \[ -\frac{1}{4 \,{\left ({\left (x + 2\right )}^{2} + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201345, size = 30, normalized size = 2.31 \[ -\frac{1}{4 \,{\left (x^{4} + 8 \, x^{3} + 26 \, x^{2} + 40 \, x + 25\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.266931, size = 22, normalized size = 1.69 \[ - \frac{1}{4 x^{4} + 32 x^{3} + 104 x^{2} + 160 x + 100} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+x)/(1+(2+x)**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.217095, size = 16, normalized size = 1.23 \[ -\frac{1}{4 \,{\left (x^{2} + 4 \, x + 5\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^3,x, algorithm="giac")
[Out]