# How do you find the indefinite integral of #int (7cosx+4e^x)dx#?

Since they're a sum, you can break it apart and integrate each part separately...

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To find the indefinite integral of ( \int (7 \cos(x) + 4e^x) , dx ), follow these steps:

- Recall the integration rules for trigonometric functions and exponential functions.
- Integrate each term separately.
- For ( \int 7 \cos(x) , dx ), use the integral formula for cosine: ( \int \cos(x) , dx = \sin(x) + C ).
- For ( \int 4e^x , dx ), use the integral formula for the exponential function: ( \int e^x , dx = e^x + C ).
- Combine the results of the integrals with the constant of integration ( C ) to get the final indefinite integral.

So, the indefinite integral of ( \int (7 \cos(x) + 4e^x) , dx ) is:

[ 7 \sin(x) + 4e^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.

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