Optimal. Leaf size=2 \[ \tan ^{-1}(x) \]
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Rubi [A]
time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {209}
\begin {gather*} \tan ^{-1}(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 209
Rubi steps
\begin {align*} \int \frac {1}{1+x^2} \, dx &=\tan ^{-1}(x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \tan ^{-1}(x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.50, size = 2, normalized size = 1.00 \begin {gather*} \text {ArcTan}\left [x\right ] \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 3, normalized size = 1.50
method | result | size |
default | \(\arctan \left (x \right )\) | \(3\) |
meijerg | \(\arctan \left (x \right )\) | \(3\) |
risch | \(\arctan \left (x \right )\) | \(3\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 2, normalized size = 1.00 \begin {gather*} \arctan \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 2, normalized size = 1.00 \begin {gather*} \arctan \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {atan}{\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \arctan x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {atan}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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