Optimal. Leaf size=9 \[ \frac {x}{1+x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {391}
\begin {gather*} \frac {x}{x^2+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 391
Rubi steps
\begin {align*} \int \frac {1-x^2}{\left (1+x^2\right )^2} \, dx &=\frac {x}{1+x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{1+x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 10, normalized size = 1.11
method | result | size |
gosper | \(\frac {x}{x^{2}+1}\) | \(10\) |
default | \(\frac {x}{x^{2}+1}\) | \(10\) |
norman | \(\frac {x}{x^{2}+1}\) | \(10\) |
risch | \(\frac {x}{x^{2}+1}\) | \(10\) |
meijerg | \(\frac {2 x}{2 x^{2}+2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{x^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.03, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{x^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 5, normalized size = 0.56 \begin {gather*} \frac {x}{x^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.51, size = 7, normalized size = 0.78 \begin {gather*} \frac {1}{x + \frac {1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{x^2+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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