int e^{(e^{x}+x)} dx= | vedclass

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(C) We are given the integral $I = \int e^{(e^{x}+x)} dx$. Using the property of exponents $e^{a+b} = e^{a} \cdot e^{b}$,we can rewrite the integral a

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

Vedclass · Answer

(C) We are given the integral $I = \int e^{(e^{x}+x)} dx$. Using the property of exponents $e^{a+b} = e^{a} \cdot e^{b}$,we can rewrite the integral as: $I = \int e^{e^{x}} \cdot e^{x} dx$. Now,let us use the method of substitution. Let $t = e^{x}$. Then,differentiating both sides with respect to $x$,we get $dt = e^{x} dx$. Substituting these into the integral,we get: $I = \int e^{t} dt$. The integral of $e^{t}$ with respect to $t$ is $e^{t} + c$. Substituting $t = e^{x}$ back into the result,we get: $I = e^{(e^{x})} + c$.

$\int e^{(e^{x}+x)} dx=$

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