$$\int\frac{\sec x\tan x}{\sqrt {e^{\sec x}}} dx$$
I let $u=\sec x$ and I already get its derivative and get $\sec x \tan x$ but I'm confused on assembling it. I get the derivative of the square root of $\sec x$. will it double my square root?
2026-05-04 14:54:06.1777906446
Evaluating the indefinite integral $\int\frac{\sec x\tan x}{\sqrt {e^{\sec x}}} dx$
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If you set $u = \sec x$, then like you say, $du = \sec x \tan x \,dx$, and so the integral becomes $$\int\frac{du}{\sqrt{e^u}} .$$ Can you rewrite the integrand in a more standard way and so recognize the integral as an elementary one?