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

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Question

(B) Let $I = \int \frac{e^x(1+x)}{\cos^2(e^x \cdot x)} dx$. Substitute $t = e^x \cdot x$. Then,by the product rule,$dt = (e^x \cdot x + e^x \cdot 1) d

Vedclass · Accepted Answer

$	an(x \cdot e^x) + c$,where $c$ is a constant of integration.

Vedclass · Answer

(B) Let $I = \int \frac{e^x(1+x)}{\cos^2(e^x \cdot x)} dx$. Substitute $t = e^x \cdot x$. Then,by the product rule,$dt = (e^x \cdot x + e^x \cdot 1) dx = e^x(x+1) dx$. Substituting these into the integral,we get: $I = \int \frac{dt}{\cos^2 t} = \int \sec^2 t dt$. The integral of $\sec^2 t$ is $	an t + c$. Therefore,$I = 	an(x \cdot e^x) + c$.

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

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