Optimal. Leaf size=21 \[ b^2 \text{CannotIntegrate}\left (\frac{e^{\sin ^{-1}(a+b x)}}{b^2 x^2},x\right ) \]
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Rubi [A] time = 0.263681, 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 = {} \[ \int \frac{e^{\sin ^{-1}(a+b x)}}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{e^{\sin ^{-1}(a+b x)}}{x^2} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{e^x \cos (x)}{\left (-\frac{a}{b}+\frac{\sin (x)}{b}\right )^2} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=\frac{\operatorname{Subst}\left (\int \frac{b^2 e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=b \operatorname{Subst}\left (\int \frac{e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\sin ^{-1}(a+b x)\right )\\ \end{align*}
Mathematica [A] time = 0.244126, size = 0, normalized size = 0. \[ \int \frac{e^{\sin ^{-1}(a+b x)}}{x^2} \, dx \]
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}^{2}}}\, 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^{2}}\,{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^{2}}, 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^{2}}\, 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^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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