What is the integral of (e^{(x^2)/2})/(x^2) ?

The integral of (e^{(x^2)/2})/(x^2) is -(e^{(x^2)/2})/(x)+(pi/2)^{1/2}\erfi(x/(sqrt(2)))+C

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integral of (e^{(x^2)/2})/(x^2)

\int \frac{e ^{\frac{x ^{2}}{2}}}{x ^{2}} d x

- \frac{e ^{\frac{x ^{2}}{2}}}{x} + (\frac{π}{2})^{\frac{1}{2}} erfi (\frac{x}{2}) + C

Solution steps

\int \frac{e ^{\frac{x ^{2}}{2}}}{x ^{2}} d x

\frac{e ^{\frac{x ^{2}}{2}}}{x ^{2}} = e^{\frac{x ^{2}}{2}} \frac{1}{x ^{2}}

= \int e^{\frac{x ^{2}}{2}} \frac{1}{x ^{2}} d x

Apply Integration By Parts

: - \frac{e ^{\frac{x ^{2}}{2}}}{x} - \int - e^{\frac{x ^{2}}{2}} d x

= - \frac{e ^{\frac{x ^{2}}{2}}}{x} - \int - e^{\frac{x ^{2}}{2}} d x

\int - e^{\frac{x ^{2}}{2}} d x = - (\frac{π}{2})^{\frac{1}{2}} erfi (\frac{x}{2})

= - \frac{e ^{\frac{x ^{2}}{2}}}{x} - (- (\frac{π}{2})^{\frac{1}{2}} erfi (\frac{x}{2}))

Simplify

= - \frac{e ^{\frac{x ^{2}}{2}}}{x} + (\frac{π}{2})^{\frac{1}{2}} erfi (\frac{x}{2})

Add a constant to the solution

= - \frac{e ^{\frac{x ^{2}}{2}}}{x} + (\frac{π}{2})^{\frac{1}{2}} erfi (\frac{x}{2}) + C

\frac{d}{d x} (3 ln (x^{2} + 1))

x + 2, \frac{1}{1 + x}, x = 2

y^{^{''}} + 7 y^{^{'}} + 10 y = 4 t e^{4 t}

f (x) = 10 x^{2}, at x = - 2

What is the integral of (e^{(x^2)/2})/(x^2) ?
The integral of (e^{(x^2)/2})/(x^2) is -(e^{(x^2)/2})/(x)+(pi/2)^{1/2}\erfi(x/(sqrt(2)))+C