The value of int e^x sec^2(e^x) , dx is | vedclass

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Question

(A) Let $I = \int e^x \sec^2(e^x) \, dx$. Substitute $t = e^x$. Then,the derivative is $dt = e^x \, dx$. Substituting these into the integral,we get:

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$	an(e^x) + k$

Vedclass · Answer

(A) Let $I = \int e^x \sec^2(e^x) \, dx$. Substitute $t = e^x$. Then,the derivative is $dt = e^x \, dx$. Substituting these into the integral,we get: $I = \int \sec^2(t) \, dt$. Since the integral of $\sec^2(t)$ is $	an(t)$,we have: $I = 	an(t) + k$. Substituting $t = e^x$ back into the expression,we get: $I = 	an(e^x) + k$.

The value of $\int e^x \sec^2(e^x) \, dx$ is

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