Optimal. Leaf size=8 \[ \text{Unintegrable}\left (\frac{1}{\tan ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.0032723, 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 = {} \[ \int \frac{1}{\tan ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\tan ^{-1}(a x)^2} \, dx &=\int \frac{1}{\tan ^{-1}(a x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.880677, size = 0, normalized size = 0. \[ \int \frac{1}{\tan ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.149, size = 0, normalized size = 0. \begin{align*} \int \left ( \arctan \left ( ax \right ) \right ) ^{-2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{a^{2} x^{2} - 2 \, a^{2} \arctan \left (a x\right ) \int \frac{x}{\arctan \left (a x\right )}\,{d x} + 1}{a \arctan \left (a x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{\arctan \left (a x\right )^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\operatorname{atan}^{2}{\left (a x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\arctan \left (a x\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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