# How do you integrate #int e^(3x)dx#?

The answer is

We need

We do this integral by substitution

Therefore,

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Undo substitution:

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To integrate ( \int e^{3x} , dx ), use the formula for integrating exponential functions:

[ \int e^{ax} , dx = \frac{1}{a} e^{ax} + C ]

Where ( a ) is a constant and ( C ) is the constant of integration. Applying this formula to the given integral:

[ \int e^{3x} , dx = \frac{1}{3} e^{3x} + C ]

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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.

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