secx dx
secxtanx
To integrate secx dx, we can use a technique called substitution.
Let u = cosx, then du/dx = -sinx and dx = du/-sinx.
Substituting u and dx in the integral, we get:
∫secx dx = ∫(1/cosx) dx
= ∫(1/u)(-sinx/du)
= -∫(sinx/u) du
Next, we can apply integration by parts to solve the integral:
Let dv = sinx du = 1/u -ln|u| + C
Substituting u back in terms of x, we get:
∫secx dx = – ln|cos(x)| + C
Therefore, the integral of secx dx is – ln|cos(x)| + C.
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