Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x \cos ^{-1}(a x)^4},x\right ) \]
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Rubi [A] time = 0.0255599, 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 = {} \[ \int \frac{1}{x \cos ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \cos ^{-1}(a x)^4} \, dx &=\int \frac{1}{x \cos ^{-1}(a x)^4} \, dx\\ \end{align*}
Mathematica [A] time = 2.79009, size = 0, normalized size = 0. \[ \int \frac{1}{x \cos ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.153, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ( \arccos \left ( ax \right ) \right ) ^{4}}}\, 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{2 \, a^{3} x^{3} \arctan \left (\sqrt{a x + 1} \sqrt{-a x + 1}, a x\right )^{3} \int \frac{{\left (2 \, a^{2} x^{2} - 3\right )} \sqrt{a x + 1} \sqrt{-a x + 1}}{{\left (a^{5} x^{6} - a^{3} x^{4}\right )} \arctan \left (\sqrt{a x + 1} \sqrt{-a x + 1}, a x\right )}\,{d x} + a x \arctan \left (\sqrt{a x + 1} \sqrt{-a x + 1}, a x\right ) + 2 \,{\left (a^{2} x^{2} + \arctan \left (\sqrt{a x + 1} \sqrt{-a x + 1}, a x\right )^{2}\right )} \sqrt{a x + 1} \sqrt{-a x + 1}}{6 \, a^{3} x^{3} \arctan \left (\sqrt{a x + 1} \sqrt{-a x + 1}, a x\right )^{3}} \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}{x \arccos \left (a x\right )^{4}}, 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}{x \operatorname{acos}^{4}{\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}{x \arccos \left (a x\right )^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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