Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x \sinh ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0131602, 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 = {} \[ \int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx &=\int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 0.540267, size = 0, normalized size = 0. \[ \int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.06, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ({\it Arcsinh} \left ( ax \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{a^{8} x^{8} + 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + a^{2} x^{2} +{\left (a^{5} x^{5} + a^{3} x^{3}\right )}{\left (a^{2} x^{2} + 1\right )}^{\frac{3}{2}} +{\left (3 \, a^{6} x^{6} + 5 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right )}{\left (a^{2} x^{2} + 1\right )} -{\left (2 \,{\left (a^{3} x^{3} + a x\right )}{\left (a^{2} x^{2} + 1\right )}^{\frac{3}{2}} +{\left (4 \, a^{4} x^{4} + 5 \, a^{2} x^{2} + 1\right )}{\left (a^{2} x^{2} + 1\right )} +{\left (2 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + a x\right )} \sqrt{a^{2} x^{2} + 1}\right )} \log \left (a x + \sqrt{a^{2} x^{2} + 1}\right ) +{\left (3 \, a^{7} x^{7} + 7 \, a^{5} x^{5} + 5 \, a^{3} x^{3} + a x\right )} \sqrt{a^{2} x^{2} + 1}}{2 \,{\left (a^{8} x^{8} + 3 \, a^{6} x^{6} +{\left (a^{2} x^{2} + 1\right )}^{\frac{3}{2}} a^{5} x^{5} + 3 \, a^{4} x^{4} + a^{2} x^{2} + 3 \,{\left (a^{6} x^{6} + a^{4} x^{4}\right )}{\left (a^{2} x^{2} + 1\right )} + 3 \,{\left (a^{7} x^{7} + 2 \, a^{5} x^{5} + a^{3} x^{3}\right )} \sqrt{a^{2} x^{2} + 1}\right )} \log \left (a x + \sqrt{a^{2} x^{2} + 1}\right )^{2}} + \int \frac{4 \,{\left (a^{4} x^{4} + 2 \, a^{2} x^{2}\right )}{\left (a^{2} x^{2} + 1\right )}^{2} +{\left (12 \, a^{5} x^{5} + 22 \, a^{3} x^{3} + 7 \, a x\right )}{\left (a^{2} x^{2} + 1\right )}^{\frac{3}{2}} + 2 \,{\left (6 \, a^{6} x^{6} + 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} + 1\right )}{\left (a^{2} x^{2} + 1\right )} +{\left (4 \, a^{7} x^{7} + 6 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + a x\right )} \sqrt{a^{2} x^{2} + 1}}{2 \,{\left (a^{10} x^{11} + 4 \, a^{8} x^{9} +{\left (a^{2} x^{2} + 1\right )}^{2} a^{6} x^{7} + 6 \, a^{6} x^{7} + 4 \, a^{4} x^{5} + a^{2} x^{3} + 4 \,{\left (a^{7} x^{8} + a^{5} x^{6}\right )}{\left (a^{2} x^{2} + 1\right )}^{\frac{3}{2}} + 6 \,{\left (a^{8} x^{9} + 2 \, a^{6} x^{7} + a^{4} x^{5}\right )}{\left (a^{2} x^{2} + 1\right )} + 4 \,{\left (a^{9} x^{10} + 3 \, a^{7} x^{8} + 3 \, a^{5} x^{6} + a^{3} x^{4}\right )} \sqrt{a^{2} x^{2} + 1}\right )} \log \left (a x + \sqrt{a^{2} x^{2} + 1}\right )}\,{d x} \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 \operatorname{arsinh}\left (a x\right )^{3}}, 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{asinh}^{3}{\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 \operatorname{arsinh}\left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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