Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\left (a^2 c x^2+c\right ) \sqrt{\tan ^{-1}(a x)}}{x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.039548, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}}{x} \, dx &=\int \frac{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}}{x} \, dx\\ \end{align*}
Mathematica [A] time = 1.61191, size = 0, normalized size = 0. \[ \int \frac{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.401, size = 0, normalized size = 0. \begin{align*} \int{\frac{{a}^{2}c{x}^{2}+c}{x}\sqrt{\arctan \left ( ax \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} c \left (\int \frac{\sqrt{\operatorname{atan}{\left (a x \right )}}}{x}\, dx + \int a^{2} x \sqrt{\operatorname{atan}{\left (a x \right )}}\, dx\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (a^{2} c x^{2} + c\right )} \sqrt{\arctan \left (a x\right )}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]