Integrand size = 12, antiderivative size = 12 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=b^2 \text {Int}\left (\frac {e^{\arcsin (a+b x)}}{b^2 x^2},x\right ) \]
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Not integrable
Time = 0.21 (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 = {} \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {e^x \cos (x)}{\left (-\frac {a}{b}+\frac {\sin (x)}{b}\right )^2} \, dx,x,\arcsin (a+b x)\right )}{b} \\ & = \frac {\text {Subst}\left (\int \frac {b^2 e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\arcsin (a+b x)\right )}{b} \\ & = b \text {Subst}\left (\int \frac {e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\arcsin (a+b x)\right ) \\ \end{align*}
Not integrable
Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
\[\int \frac {{\mathrm e}^{\arcsin \left (b x +a \right )}}{x^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int \frac {e^{\operatorname {asin}{\left (a + b x \right )}}}{x^{2}}\, dx \]
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Not integrable
Time = 0.45 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int { \frac {e^{\left (\arcsin \left (b x + a\right )\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\arcsin (a+b x)}}{x^2} \, dx=\int \frac {{\mathrm {e}}^{\mathrm {asin}\left (a+b\,x\right )}}{x^2} \,d x \]
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