Optimal. Leaf size=22 \[ b^2 \text {Int}\left (\frac {e^{\text {ArcSin}(a+b x)}}{b^2 x^2},x\right ) \]
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Rubi [A]
time = 0.20, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{\text {ArcSin}(a+b x)}}{x^2} \, dx \end {gather*}
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 {\text {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 {\text {Subst}\left (\int \frac {b^2 e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\sin ^{-1}(a+b x)\right )}{b}\\ &=b \text {Subst}\left (\int \frac {e^x \cos (x)}{(a-\sin (x))^2} \, dx,x,\sin ^{-1}(a+b x)\right )\\ \end {align*}
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Mathematica [A]
time = 0.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\text {ArcSin}(a+b x)}}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{\arcsin \left (b x +a \right )}}{x^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\operatorname {asin}{\left (a + b x \right )}}}{x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{\mathrm {asin}\left (a+b\,x\right )}}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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