int e^{x} sec x(1+tan x) d x equals | vedclass

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Question

(D) We are given the integral $I = \int e^{x} \sec x(1+	an x) d x$.Distributing the term $\sec x$,we get:$I = \int e^{x}(\sec x + \sec x 	an x) d x$

Vedclass · Accepted Answer

$e^{x} \sec x+C$

Vedclass · Answer

(D) We are given the integral $I = \int e^{x} \sec x(1+	an x) d x$.Distributing the term $\sec x$,we get:$I = \int e^{x}(\sec x + \sec x 	an x) d x$.Recall the standard integration formula: $\int e^{x} \{f(x) + f'(x)\} d x = e^{x} f(x) + C$.Let $f(x) = \sec x$. Then,the derivative $f'(x) = \frac{d}{dx}(\sec x) = \sec x 	an x$.Substituting these into the formula,we obtain:$I = e^{x} \sec x + C$.Thus,the correct option is $D$.

$\int e^{x} \sec x(1+\tan x) d x$ equals

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