(B) We know the standard integral form $\int e^{x} [f(x) + f'(x)] dx = e^{x} f(x) + c$.Given the integral $\int e^{x} \sec x(1+\tan x) dx$.Distributin

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(B) We know the standard integral form $\int e^{x} [f(x) + f'(x)] dx = e^{x} f(x) + c$.Given the integral $\int e^{x} \sec x(1+\tan x) dx$.Distributing $\sec x$,we get $\int e^{x} (\sec x + \sec x \tan x) dx$.Let $f(x) = \sec x$. Then $f'(x) = \sec x \tan x$.Substituting this into the standard form,we get $e^{x} \sec x + c$.