Integral of tan x

In this paper, we will discuss how to integrate the following tan (x). The technique used is the integration of substitution techniques.

$ ∫ tan (x) dx = ∫ frac{sin (x)}{cos (x)} dx $

Notice the integran on the right, we can assume u = cos (x) because the derivatives of cos (x) are sin (x).

If u = cos (x) then du = sin (x) dx so we get:

$ begin{align} ∫ tan (x) dx &= ∫ frac{sin (x)}{cos (x)} dx \ &= ∫ frac{du}{u} \ &= ln (u) \ &= ln (cos x) end{align} $

So, $ ∫ tan (x) dx = ln (cos x) + C $

Note:
$ ∫ frac{1}{x} dx = ln (x) + C $
ln: natural logarithm.

Hopefully this article useful for readers.

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