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

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Question

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

Vedclass · Accepted Answer

$	an(x e^{x}) + c$

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(B) Let $I = \int \frac{e^{x}(1+x) dx}{\cos^{2}(x e^{x})}$.Substitute $t = x e^{x}$.Then,$dt = (1 \cdot e^{x} + x \cdot e^{x}) dx = e^{x}(1+x) dx$.Substituting these into the integral,we get $I = \int \frac{dt}{\cos^{2} t}$.$I = \int \sec^{2} t dt$.Integrating $\sec^{2} t$,we get $I = 	an t + c$.Substituting back $t = x e^{x}$,we get $I = 	an(x e^{x}) + c$.

The value of $\int \frac{e^{x}(1+x) dx}{\cos^{2}(x e^{x})}$ is equal to

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