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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