Integrand size = 23, antiderivative size = 23 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\text {Int}\left (\frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}},x\right ) \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx \\ \end{align*}
Not integrable
Time = 0.47 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx \]
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Not integrable
Time = 0.18 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
\[\int \frac {x^{m} \operatorname {arcsinh}\left (a x \right )^{3}}{\sqrt {a^{2} x^{2}+1}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int { \frac {x^{m} \operatorname {arsinh}\left (a x\right )^{3}}{\sqrt {a^{2} x^{2} + 1}} \,d x } \]
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Not integrable
Time = 2.54 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int \frac {x^{m} \operatorname {asinh}^{3}{\left (a x \right )}}{\sqrt {a^{2} x^{2} + 1}}\, dx \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int { \frac {x^{m} \operatorname {arsinh}\left (a x\right )^{3}}{\sqrt {a^{2} x^{2} + 1}} \,d x } \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int { \frac {x^{m} \operatorname {arsinh}\left (a x\right )^{3}}{\sqrt {a^{2} x^{2} + 1}} \,d x } \]
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Not integrable
Time = 2.55 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx=\int \frac {x^m\,{\mathrm {asinh}\left (a\,x\right )}^3}{\sqrt {a^2\,x^2+1}} \,d x \]
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