Optimal. Leaf size=10 \[ \frac {\tan ^{-1}\left (\frac {x}{a}\right )}{a} \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {203} \[ \frac {\tan ^{-1}\left (\frac {x}{a}\right )}{a} \]
Antiderivative was successfully verified.
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Rule 203
Rubi steps
\begin {align*} \int \frac {1}{a^2+x^2} \, dx &=\frac {\tan ^{-1}\left (\frac {x}{a}\right )}{a}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ \frac {\tan ^{-1}\left (\frac {x}{a}\right )}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 10, normalized size = 1.00 \[ \frac {\arctan \left (\frac {x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 10, normalized size = 1.00 \[ \frac {\arctan \left (\frac {x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 1.10 \[ \frac {\arctan \left (\frac {x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.99, size = 10, normalized size = 1.00 \[ \frac {\arctan \left (\frac {x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.25, size = 10, normalized size = 1.00 \[ \frac {\mathrm {atan}\left (\frac {x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 0.11, size = 20, normalized size = 2.00 \[ \frac {- \frac {i \log {\left (- i a + x \right )}}{2} + \frac {i \log {\left (i a + x \right )}}{2}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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