Integrand size = 7, antiderivative size = 2 \[ \int \frac {1}{1+x^2} \, dx=\arctan (x) \]
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Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {209} \[ \int \frac {1}{1+x^2} \, dx=\arctan (x) \]
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Rule 209
Rubi steps \begin{align*} \text {integral}& = \arctan (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\arctan (x) \]
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Time = 0.06 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.50
method | result | size |
default | \(\arctan \left (x \right )\) | \(3\) |
meijerg | \(\arctan \left (x \right )\) | \(3\) |
risch | \(\arctan \left (x \right )\) | \(3\) |
parallelrisch | \(\frac {i \ln \left (x +i\right )}{2}-\frac {i \ln \left (x -i\right )}{2}\) | \(18\) |
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none
Time = 0.24 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\arctan \left (x\right ) \]
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Time = 0.04 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\operatorname {atan}{\left (x \right )} \]
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none
Time = 0.28 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\arctan \left (x\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\arctan \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {1}{1+x^2} \, dx=\mathrm {atan}\left (x\right ) \]
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