Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{a^2 c x^2+c}{\tan ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.0122972, 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 = {} \[ \int \frac{c+a^2 c x^2}{\tan ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{c+a^2 c x^2}{\tan ^{-1}(a x)^2} \, dx &=\int \frac{c+a^2 c x^2}{\tan ^{-1}(a x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.542987, size = 0, normalized size = 0. \[ \int \frac{c+a^2 c x^2}{\tan ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.757, size = 0, normalized size = 0. \begin{align*} \int{\frac{{a}^{2}c{x}^{2}+c}{ \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^{4} c x^{4} + 2 \, a^{2} c x^{2} - 4 \, a \arctan \left (a x\right ) \int \frac{a^{3} c x^{3} + a c x}{\arctan \left (a x\right )}\,{d x} + c}{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{a^{2} c x^{2} + c}{\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*} c \left (\int \frac{a^{2} x^{2}}{\operatorname{atan}^{2}{\left (a x \right )}}\, dx + \int \frac{1}{\operatorname{atan}^{2}{\left (a x \right )}}\, dx\right ) \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{a^{2} c x^{2} + c}{\arctan \left (a x\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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