3.11.20 \(\int (x+\frac {1-x^2}{1+x}) \, dx\) [1020]

Optimal. Leaf size=1 \[ x \]

[Out]

x

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Rubi [A]
time = 0.00, antiderivative size = 1, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x + (1 - x^2)/(1 + x),x]

[Out]

x

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Maple [A]
time = 0.22, size = 2, normalized size = 2.00

method	result	size
default	\(x\)	\(2\)
norman	\(x\)	\(2\)
risch	\(x\)	\(2\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x+(-x^2+1)/(1+x),x,method=_RETURNVERBOSE)

[Out]

x

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Maxima [A]
time = 0.27, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}

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 = 0.34, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}

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 = 0.01, size = 0, normalized size = 0.00 \begin {gather*} x \end {gather*}

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 = 1.98, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x

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Mupad [B]
time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x - (x^2 - 1)/(x + 1),x)

[Out]

x

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