How to determine the indefinite integral of e^square rootx/square rootx (substitution or parts) ?

We'll integrate using substitution or we'll change the
variable. For this reason, we'll consider the
formula:

We'll note sqrtx =
t.

We'll differentiate both
sides:

dx/2sqrtx = dt

dx/sqrtx
= 2dt

We'll re-write the integral in
t:

Int e^t*2dt = 2e^t +
C

We'll substitute t by sqrt
x:

Int e^sqrtx*dx/sqrtx = 2e^sqrtx +
C

The indefinite integral is evaluated using substitution
and the result is:

Int e^sqrtx*dx/sqrtx =
2e^sqrtx + C