How do you integrate #int (e^(2x)+2e^x+1)/(e^x)dx#?
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To integrate (\int \frac{e^{2x} + 2e^x + 1}{e^x} , dx), you can simplify the expression in the numerator by factoring out (e^x). This yields:
(\int \frac{e^{2x} + 2e^x + 1}{e^x} , dx = \int (e^x + 2 + \frac{1}{e^x}) , dx).
Then, integrate each term separately:
(\int e^x , dx = e^x + C_1),
(\int 2 , dx = 2x + C_2),
(\int \frac{1}{e^x} , dx = -e^{-x} + C_3).
Where (C_1), (C_2), and (C_3) are constants of integration.
Therefore, the integral becomes:
(e^x + 2x - e^{-x} + C),
Where (C) is the constant of integration.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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