Mastering Integration Of Trigonometric Functions Using Substitution Technique

secx dx

secxtanx

This integral involves trigonometric functions. We can solve it by using substitution.

Let’s begin by substituting u = sec x. To do this, we need to know the derivative of sec x, which is sec x tan x.

Therefore,

du/dx = sec x tan x

dx = du/sec x

Now we can replace sec x dx with du. So,

∫sec x dx = ∫(1/u) du

Integrating 1/u with respect to u gives us:

ln |u| + C

where C is the constant of integration.

Substituting back u = sec x, we get:

ln |sec x| + C

So, the final solution to the integral is:

∫sec x dx = ln |sec x| + C.

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