integrate (1/(sqrt x)) (e^-x) dxI've got no idea how to do this.

1 Answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should use substitution to evaluate the integral such that:

`sqrtx = t => 1/(2sqrtx)dx = dt => dx = 2tdt`

Changing the variable to integrand yields:

`int (e^(-x))/(sqrt x) dx = int ((e^(-t^2))/t)*2tdt`

`int (e^(-x))/(sqrt x) dx = 2int ((e^(-t^2)) dt`

You should remember the definition of the special function called error function such that:

`erf(x) = 2/(sqrt pi) int_0^(pi) ((e^(-t^2)) dt `

Hence, evaluating the given integral yields `sqrt pi*(erf(x))/2` .