Integral of $$$e^{i n p t}$$$ with respect to $$$x$$$
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Your Input
Find $$$\int e^{i n p t}\, dx$$$.
Solution
Apply the constant rule $$$\int c\, dx = c x$$$ with $$$c=e^{i n p t}$$$:
$${\color{red}{\int{e^{i n p t} d x}}} = {\color{red}{x e^{i n p t}}}$$
Therefore,
$$\int{e^{i n p t} d x} = x e^{i n p t}$$
Add the constant of integration:
$$\int{e^{i n p t} d x} = x e^{i n p t}+C$$
Answer
$$$\int e^{i n p t}\, dx = x e^{i n p t} + C$$$A
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