int frac{e^x(x + 1)}{cos^2(x e^x)} dx = | vedclass

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Question

(A) Let $I = \int \frac{e^x(x + 1)}{\cos^2(x e^x)} dx$. We can rewrite the integral as $I = \int e^x(x + 1) \sec^2(x e^x) dx$. Let $t = x e^x$. Then,d

Vedclass · Accepted Answer

$	an(x e^x) + c$

Vedclass · Answer

(A) Let $I = \int \frac{e^x(x + 1)}{\cos^2(x e^x)} dx$. We can rewrite the integral as $I = \int e^x(x + 1) \sec^2(x e^x) dx$. Let $t = x e^x$. Then,differentiating with respect to $x$ using the product rule,we get $dt = (1 \cdot e^x + x \cdot e^x) dx = e^x(1 + x) dx$. Substituting these into the integral,we get $I = \int \sec^2(t) dt$. The integral of $\sec^2(t)$ is $	an(t) + c$. Substituting back $t = x e^x$,we get $I = 	an(x e^x) + c$.

$\int \frac{e^x(x + 1)}{\cos^2(x e^x)} dx = $

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