Integrand size = 27, antiderivative size = 27 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\text {Int}\left (\frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 27, 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 = {} \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx \\ \end{align*}
Not integrable
Time = 0.55 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.93
\[\int \frac {x^{m}}{\sqrt {c^{2} x^{2}+1}\, \left (a +b \,\operatorname {arcsinh}\left (c x \right )\right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.63 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int { \frac {x^{m}}{\sqrt {c^{2} x^{2} + 1} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.86 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int \frac {x^{m}}{\left (a + b \operatorname {asinh}{\left (c x \right )}\right ) \sqrt {c^{2} x^{2} + 1}}\, dx \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int { \frac {x^{m}}{\sqrt {c^{2} x^{2} + 1} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int { \frac {x^{m}}{\sqrt {c^{2} x^{2} + 1} {\left (b \operatorname {arsinh}\left (c x\right ) + a\right )}} \,d x } \]
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Not integrable
Time = 2.79 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx=\int \frac {x^m}{\left (a+b\,\mathrm {asinh}\left (c\,x\right )\right )\,\sqrt {c^2\,x^2+1}} \,d x \]
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