3.882 \(\int \left (x+\frac{1-x^2}{1+x}\right ) \, dx\)

Optimal. Leaf size=1 \[ x \]

[Out]

x

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Rubi [A]  time = 0.00524836, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ x \]

Antiderivative was successfully verified.

[In]  Int[x + (1 - x^2)/(1 + x),x]

[Out]

x

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Rubi in Sympy [A]  time = 1.68149, size = 0, normalized size = 0. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x+(-x**2+1)/(1+x),x)

[Out]

x

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Mathematica [A]  time = 0.000289905, size = 1, normalized size = 1. \[ x \]

Antiderivative was successfully verified.

[In]  Integrate[x + (1 - x^2)/(1 + x),x]

[Out]

x

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Maple [A]  time = 0.001, size = 2, normalized size = 2. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x+(-x^2+1)/(1+x),x)

[Out]

x

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Maxima [A]  time = 0.694714, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x - (x^2 - 1)/(x + 1),x, algorithm="maxima")

[Out]

x

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Fricas [A]  time = 0.24318, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x - (x^2 - 1)/(x + 1),x, algorithm="fricas")

[Out]

x

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Sympy [A]  time = 0.064693, size = 0, normalized size = 0. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x+(-x**2+1)/(1+x),x)

[Out]

x

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GIAC/XCAS [A]  time = 0.27403, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x - (x^2 - 1)/(x + 1),x, algorithm="giac")

[Out]

x