To integrate secx tanx dx, we can use a substitution method. Setting u = secx + tanx, we can find du/dx = secx tanx + sec^2x = u^2. So we have:
secx tanx dx = du/u^2
Integrating with respect to u, we get:
∫ secx tanx dx = ∫ du/u^2 = -1/u + C
Substituting back u = secx + tanx, we have:
∫ secx tanx dx = -1/(secx + tanx) + C
This is our final answer.
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