int e^x cdot sec x(1+tan x) , dx = . . . . | vedclass

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(B) We know that the integral of the form $\int e^x [f(x) + f'(x)] \, dx = e^x f(x) + C$. Given the integral is $\int e^x \cdot \sec x(1 + 	an x) \,

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$e^x \cdot \sec x$

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(B) We know that the integral of the form $\int e^x [f(x) + f'(x)] \, dx = e^x f(x) + C$. Given the integral is $\int e^x \cdot \sec x(1 + 	an x) \, dx$. This can be rewritten as $\int e^x (\sec x + \sec x 	an x) \, dx$. Here,let $f(x) = \sec x$. Then,the derivative $f'(x) = \sec x 	an x$. Substituting these into the formula,we get $\int e^x (f(x) + f'(x)) \, dx = e^x \sec x + C$. Therefore,the correct option is $B$.

$\int e^x \cdot \sec x(1+\tan x) \, dx = $ . . . . . . $+ C$.

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