3.1020 \(\int (x+\frac{1-x^2}{1+x}) \, dx\)

Optimal. Leaf size=1 \[ x \]

[Out]

x

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Rubi [A]  time = 0.0014713, 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., Rules used = {} \[ x \]

Antiderivative was successfully verified.

[In]

Int[x + (1 - x^2)/(1 + x),x]

[Out]

x

Rubi steps

\begin{align*} \int \left (x+\frac{1-x^2}{1+x}\right ) \, dx &=x\\ \end{align*}

Mathematica [A]  time = 0.0001636, 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., size = 2, normalized size = 2. \begin{align*} x \end{align*}

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 = 1.01128, size = 1, normalized size = 1. \begin{align*} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x

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Fricas [A]  time = 1.62357, size = 4, normalized size = 4. \begin{align*} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x

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Sympy [A]  time = 0.052979, size = 0, normalized size = 0. \begin{align*} x \end{align*}

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 [A]  time = 1.13023, size = 1, normalized size = 1. \begin{align*} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x