Integrand size = 17, antiderivative size = 17 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=-\frac {e^{a+b x-c x^2}}{x}+\sqrt {c} e^{a+\frac {b^2}{4 c}} \sqrt {\pi } \text {erf}\left (\frac {b-2 c x}{2 \sqrt {c}}\right )+b \text {Int}\left (\frac {e^{a+b x-c x^2}}{x},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 17, 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 = {} \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int \frac {e^{a+b x-c x^2}}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {e^{a+b x-c x^2}}{x}+b \int \frac {e^{a+b x-c x^2}}{x} \, dx-(2 c) \int e^{a+b x-c x^2} \, dx \\ & = -\frac {e^{a+b x-c x^2}}{x}+b \int \frac {e^{a+b x-c x^2}}{x} \, dx-\left (2 c e^{a+\frac {b^2}{4 c}}\right ) \int e^{-\frac {(b-2 c x)^2}{4 c}} \, dx \\ & = -\frac {e^{a+b x-c x^2}}{x}+\sqrt {c} e^{a+\frac {b^2}{4 c}} \sqrt {\pi } \text {erf}\left (\frac {b-2 c x}{2 \sqrt {c}}\right )+b \int \frac {e^{a+b x-c x^2}}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.33 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int \frac {e^{a+b x-c x^2}}{x^2} \, dx \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94
\[\int \frac {{\mathrm e}^{-c \,x^{2}+b x +a}}{x^{2}}d x\]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 2.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=e^{a} \int \frac {e^{b x} e^{- c x^{2}}}{x^{2}}\, dx \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int { \frac {e^{\left (-c x^{2} + b x + a\right )}}{x^{2}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{a+b x-c x^2}}{x^2} \, dx=\int \frac {{\mathrm {e}}^{-c\,x^2+b\,x+a}}{x^2} \,d x \]
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