Optimal. Leaf size=15 \[ x \tan ^{-1}(x)-\frac {1}{2} \log \left (x^2+1\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {4846, 260} \[ x \tan ^{-1}(x)-\frac {1}{2} \log \left (x^2+1\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rule 4846
Rubi steps
\begin {align*} \int \tan ^{-1}(x) \, dx &=x \tan ^{-1}(x)-\int \frac {x}{1+x^2} \, dx\\ &=x \tan ^{-1}(x)-\frac {1}{2} \log \left (1+x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ x \tan ^{-1}(x)-\frac {1}{2} \log \left (x^2+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 13, normalized size = 0.87 \[ x \arctan \relax (x) - \frac {1}{2} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 13, normalized size = 0.87 \[ x \arctan \relax (x) - \frac {1}{2} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \[ x \arctan \relax (x )-\frac {\ln \left (x^{2}+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 13, normalized size = 0.87 \[ x \arctan \relax (x) - \frac {1}{2} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 13, normalized size = 0.87 \[ x\,\mathrm {atan}\relax (x)-\frac {\ln \left (x^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 12, normalized size = 0.80 \[ x \operatorname {atan}{\relax (x )} - \frac {\log {\left (x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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