Integrand size = 12, antiderivative size = 12 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=b \text {Int}\left (\frac {e^{\arcsin (a+b x)}}{b x},x\right ) \]
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Not integrable
Time = 0.14 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int \frac {e^{\arcsin (a+b x)}}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {e^x \cos (x)}{-\frac {a}{b}+\frac {\sin (x)}{b}} \, dx,x,\arcsin (a+b x)\right )}{b} \\ & = \frac {\text {Subst}\left (\int \frac {b e^x \cos (x)}{-a+\sin (x)} \, dx,x,\arcsin (a+b x)\right )}{b} \\ & = \text {Subst}\left (\int \frac {e^x \cos (x)}{-a+\sin (x)} \, dx,x,\arcsin (a+b x)\right ) \\ \end{align*}
Not integrable
Time = 0.13 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int \frac {e^{\arcsin (a+b x)}}{x} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
\[\int \frac {{\mathrm e}^{\arcsin \left (b x +a \right )}}{x}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int \frac {e^{\operatorname {asin}{\left (a + b x \right )}}}{x}\, dx \]
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Not integrable
Time = 0.45 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x} \,d x } \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x} \, dx=\int \frac {{\mathrm {e}}^{\mathrm {asin}\left (a+b\,x\right )}}{x} \,d x \]
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