## ∫ sec²(x) dx

### To find the integral of sec^2(x) dx, we use a method called integration by substitution

To find the integral of sec^2(x) dx, we use a method called integration by substitution.

First, we need to choose our substitution. Let’s choose u = tan(x).

To find du/dx, we differentiate both sides of the equation u = tan(x) with respect to x:

du/dx = sec^2(x)

This is exactly what we need to replace sec^2(x) in our original integral. Rearranging the equation, we have:

du = sec^2(x) dx

Now we can replace sec^2(x) dx in the original integral with du:

∫ sec^2(x) dx = ∫ du

Integrating du is straightforward:

∫ du = u + C

Substituting u back in terms of x, we have:

∫ sec^2(x) dx = tan(x) + C

Therefore, the integral of sec^2(x) dx is tan(x) + C, where C is the constant of integration.

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