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Integration of e^radicalx / radicalx dx
To integrate the function ∫ e^√x/√x dx, we can use a method called substitution.
Let's start by making a substitution:
Let u = √x
This implies du/dx = 1/(2√x)
Now, we need to express the original function in terms of u, so let's solve for x in terms of u:
x = u^2
Next, we'll need to compute dx in terms of du:
dx = 2u du
Substituting the values of u, x, and dx into the original integral, we get:
∫ e^√x/√x dx = ∫ e^u/u * 2u du
Simplifying, we have:
∫ 2e^u du
Now, we can integrate this expression easily.
The integral of 2e^u du is simply 2e^u.
So, the final result is:
∫ e^√x/√x dx = 2e^u + C
But remember, we need to substitute back for u in terms of x.
So our final answer is:
2e^√x + C, where C is the constant of integration.