Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\frac{1}{x \left (a+b \cos ^{-1}(c x)\right )^3},x\right ) \]
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Rubi [A] time = 0.0226184, 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 = {} \[ \int \frac{1}{x \left (a+b \cos ^{-1}(c x)\right )^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \left (a+b \cos ^{-1}(c x)\right )^3} \, dx &=\int \frac{1}{x \left (a+b \cos ^{-1}(c x)\right )^3} \, dx\\ \end{align*}
Mathematica [A] time = 3.37358, size = 0, normalized size = 0. \[ \int \frac{1}{x \left (a+b \cos ^{-1}(c x)\right )^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.317, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ( a+b\arccos \left ( cx \right ) \right ) ^{3}}}\, 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{\sqrt{c x + 1} \sqrt{-c x + 1} b c x + b \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right ) + a + \frac{2 \,{\left (b^{4} c^{2} x^{2} \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right )^{2} + 2 \, a b^{3} c^{2} x^{2} \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right ) + a^{2} b^{2} c^{2} x^{2}\right )} \int \frac{1}{{\left (b \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right ) + a\right )} x^{3}}\,{d x}}{b^{2} c^{2}}}{2 \,{\left (b^{4} c^{2} x^{2} \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right )^{2} + 2 \, a b^{3} c^{2} x^{2} \arctan \left (\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right ) + a^{2} b^{2} c^{2} x^{2}\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}{b^{3} x \arccos \left (c x\right )^{3} + 3 \, a b^{2} x \arccos \left (c x\right )^{2} + 3 \, a^{2} b x \arccos \left (c x\right ) + a^{3} x}, 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 \left (a + b \operatorname{acos}{\left (c x \right )}\right )^{3}}\, 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}{{\left (b \arccos \left (c x\right ) + a\right )}^{3} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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