Evaluate #int_0^∞(e^(-sqrt(x))/(sqrtx))dx# ?

1 Answer
Cesareo R.
Sep 12, 2017

See below.

Explanation:

Following your steps.

#int_0^∞(e^(-sqrt(x))/(sqrtx))dx#

#u=-sqrt(x)#
#du=-(dx)/(2sqrt(x))=1/2dx/u#

#int_0^∞(e^(-sqrt(x))/(sqrtx))dx=-2int_0^(-∞) e^u du#

note that as #x->oo# we have #u->-oo#

#=-2[e^u]_0^(-oo)=2#

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