∫(secx)dx
To find the integral of sec(x) with respect to x, we can use a method called integration by substitution
To find the integral of sec(x) with respect to x, we can use a method called integration by substitution. The first step is to identify a suitable substitution:
Let’s set u = tan(x) + sec(x). Then, calculating du/dx:
du/dx = sec^2(x) + sec(x)tan(x).
Rearranging this equation, we have:
du = (sec^2(x) + sec(x)tan(x)) dx.
Now, let’s substitute these values into our original integral:
∫(sec(x)) dx = ∫(sec^2(x) + sec(x)tan(x)) dx.
Using our substitution, sec(x)dx = du, and sec^2(x) + sec(x)tan(x) dx = du. Our integral then becomes:
∫ du.
The integral of du is simply u + C, where C is the constant of integration. Substituting back in for u, we get:
∫(sec(x)) dx = tan(x) + sec(x) + C.
So, the indefinite integral of sec(x) with respect to x is equal to tan(x) + sec(x) + C, where C represents the constant of integration.
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