Optimal. Leaf size=19 \[ b \text{CannotIntegrate}\left (\frac{e^{\sin ^{-1}(a+b x)}}{b x},x\right ) \]
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Rubi [A] time = 0.199484, 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 = {} \[ \int \frac{e^{\sin ^{-1}(a+b x)}}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{e^{\sin ^{-1}(a+b x)}}{x} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{e^x \cos (x)}{-\frac{a}{b}+\frac{\sin (x)}{b}} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=\frac{\operatorname{Subst}\left (\int \frac{b e^x \cos (x)}{-a+\sin (x)} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=\operatorname{Subst}\left (\int \frac{e^x \cos (x)}{-a+\sin (x)} \, dx,x,\sin ^{-1}(a+b x)\right )\\ \end{align*}
Mathematica [A] time = 0.11501, size = 0, normalized size = 0. \[ \int \frac{e^{\sin ^{-1}(a+b x)}}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.007, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{\arcsin \left ( bx+a \right ) }}}{x}}\, 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*} \int \frac{e^{\left (\arcsin \left (b x + a\right )\right )}}{x}\,{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{e^{\left (\arcsin \left (b x + a\right )\right )}}{x}, 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{e^{\operatorname{asin}{\left (a + b x \right )}}}{x}\, 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{e^{\left (\arcsin \left (b x + a\right )\right )}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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