# �ç e^�ãx / �ãx dx

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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.