Optimal. Leaf size=10 \[ \frac{\tan ^{-1}\left (\frac{x}{c}\right )}{c} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0024157, antiderivative size = 10, normalized size of antiderivative = 1., 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} \[ \frac{\tan ^{-1}\left (\frac{x}{c}\right )}{c} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 203
Rubi steps
\begin{align*} \int \frac{1}{c^2+x^2} \, dx &=\frac{\tan ^{-1}\left (\frac{x}{c}\right )}{c}\\ \end{align*}
Mathematica [A] time = 0.0023078, size = 10, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{x}{c}\right )}{c} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 11, normalized size = 1.1 \begin{align*}{\frac{1}{c}\arctan \left ({\frac{x}{c}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.4306, size = 14, normalized size = 1.4 \begin{align*} \frac{\arctan \left (\frac{x}{c}\right )}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.87814, size = 20, normalized size = 2. \begin{align*} \frac{\arctan \left (\frac{x}{c}\right )}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [C] time = 0.104491, size = 20, normalized size = 2. \begin{align*} \frac{- \frac{i \log{\left (- i c + x \right )}}{2} + \frac{i \log{\left (i c + x \right )}}{2}}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06632, size = 14, normalized size = 1.4 \begin{align*} \frac{\arctan \left (\frac{x}{c}\right )}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]