$\int e^{e^{x} + x} d x =$

e^{e^{x}} + x + c

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e^{e^{x}} + c

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e^{x} + c

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e^{x} + x + c

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Solution

The correct option is B $e^{e^{x}} + c$
The expression $e^{e^{x} + x}$ can be written as $e^{e^{x}} e^{x}$
Thus, $\int e^{e^{x} + x} d x = \int e^{e^{x}} e^{x} d x$
Let $e^{x} = t$
Differentiating both sides,
$e^{x} d x = d t$
Substituting it back in the expression,
$\int e^{t} d t = e^{t} + c$
Putting back the value of $t$ in the expression,
$=$ $e^{e^{x}} + c$

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